Flirting with Models

The Research Library of Newfound Research

Category: Risk Management Page 10 of 11

Portable Beta: Making the Most of the Returns You’re Already Getting

By

On December 4, 2017

In Podcast, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary­­

  • Traditionally, investors have used a balance between stocks and bonds to govern their asset allocation. Expanding this palette to include other asset classes can allow them to potentially both enhance return and reduce risk, benefiting from diversification.
  • Modern portfolio theory tells us, however, that the truly optimal choice is to apply leverage to the most risk-efficient portfolio.
  • In a low expected return environment, we believe that capital efficiency is of the utmost importance, allowing investors to better capture the returns they are already earning.
  • We believe that the select application of leverage can allow investors to both benefit from enhanced diversification and capital efficiency, in a concept we are calling portable beta.

Diversification has been the cornerstone of investing for thousands of years as evidenced by timeless proverbs like “don’t put all your eggs in one basket.” The magic behind diversification – and one of the reasons it is considered the only “free lunch” available in investing – is that a portfolio of assets will always have a risk level less-than-or-equal-to the riskiest asset within the portfolio.

Yet it was not until Dr. Harry Markowitz published his seminal article “Portfolio Selection” in 1952 that investors had a mathematical formulation for the concept. His work, which ultimately coalesced into Modern Portfolio Theory (MPT), not only provided practitioners a means to measure risk and diversification, but it also allowed them to quantify the marginal benefit of adding new exposures to a portfolio and to derive optimal investment portfolios. For his work, Dr. Markowitz was awarded a Nobel prize in 1990.

What became apparent through this work is that the risk and expected reward trade-off is not necessarily linear.  For example, in shifting a portfolio’s allocations from 100% bonds to 100% stocks, risk may actually initially decrease and expected return may increase due to diversification benefits.  For example, in the hypothetical image below, we can see that the 60/40 stock-bond blend offers a nearly identical risk level to the 100% bond portfolio with significantly higher expected return.

Of course, these benefits are not limited solely to stock/bond mixes.  Indeed, many investors focus on how they can expand their investment palette beyond traditional asset classes to include exposures that can expand the efficient frontier: the set of portfolios that represents the maximum expected return for each given risk level.

In the example graph below we can see this expectation labeled as the diversification benefit.

The true spirit of MPT suggests something different, however.  MPT argues that in an efficient market, all investors would hold an identically allocated portfolio, which turns out to be the market portfolio. Holding any other portfolio would be sub-optimal.  The argument goes that rational investors would all seek to maximize their expected risk-adjusted return and then simply introduce cash or leverage to meet their desired risk preference.  This notion is laid out below.

In practice, however, while many investors are willing to expand their investment palette beyond just stocks and bonds, few ultimately take this last step of adding leverage.  Conservative investors rarely barbell a riskier portfolio with cash, instead opting to be fully invested in fixed income centric portfolios.  Aggressive investors rarely apply leverage, instead increasing their allocation to risky assets.  Some argue that this leverage aversion actually gives rise to the low volatility / betting-against-beta anomaly.

This is unfortunate, as the prudent use of leverage can potentially enhance returns without necessarily increasing risk.  For example, below we plot the hypothetical growth of a dollar invested in the S&P 500, a 60/40 portfolio, and a 60/40 portfolio levered to target the volatility level of the S&P 500.

Ann. ReturnAnn. VolatilityMax Drawdown
S&P 5009.2%14.1%55.2%
60/40 Portfolio8.0%7.7%29.8%
Levered 60/40 Portfolio12.5%14.9%54.4%

Source: CSI.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees except for underlying ETF expense ratios.  The S&P 500 represented by SPDR S&P 500 ETF (”SPY”).  60/40 Portfolio is a 60% SPDR S&P 500 ETF (“SPY”) and 40% iShares 7-10 Year U.S. Treasury ETF (“IEF”) mix, rebalanced annually.  Levered 60/40 applies 182% leverage to the 60/40 Portfolio by shorting an 82% position in the iShares 1-3 Year U.S. Treasury ETF (“SHY”).  The leverage amount was selected so that the Levered 60/40 Portfolio would match the annualized volatility level of the S&P 500.

We can see that the Levered 60/40 portfolio trounces the S&P 500, despite sharing nearly identical risk levels.  The answer as to why is two-fold.

First is the diversification benefits we gain from introducing a negatively correlated asset to a 100% equity portfolio.  We can see this by comparing the annualized return and volatility of the S&P 500 versus the standard 60/40 portfolio.  While the S&P 500 outperformed by 120 bps per year, it required bearing 640 bps of excess volatility (14.9% vs. 7.7%) and a realized drawdown that was of 2540 bps deeper (55.2% vs. 29.8%).  Introducing the diversifying asset made the portfolio more risk-efficient.  Unfortunately, in doing so, we were forced to allocate to an asset with a lower expected return (from equities to bonds), causing us to realize a lower return.

This lower return but higher risk-adjusted return is the thinking behind the common saying that “investors can’t eat risk-adjusted returns.”

That is where the benefits from leverage come into play.  Leverage creates capital efficiency.  In this example, we were able to treat each $1 invested as if it were $1.82.  This allowed us to match the risk level of equities and benefit from the enhanced risk-efficiency of the diversified portfolio.

Efficiency Over Alpha

In a recent Barron’s roundtable[1], we were asked our thoughts on the future of ETFs.  We receive this question fairly often when speaking on panels.  The easy, obvious answers are, “more niche products,” or “an ETF for every asset class,” or even “smarter beta” (as if somehow beta has gone from high school to college and is now matriculating to graduate school).

In truth, none of these answers seem particularly innovative or even satisfactory when we consider that they will likely do little to help investors actually achieve their financial goals.  This is especially true in a low expected return environment, where finding the balance between growth and safety is akin to sailing between Scylla and Charybdis[2]: too much exposure to risky assets can increase sequence risk and too little can increase longevity risk.  Edging too close to either can spell certain financial doom.

With this in mind, our answer as of late has deviated from tradition and instead has focused on greater efficiency.  Instead of trying to pursue excess returns, our answer is to maximize the returns investors are, largely, getting already.  Here are a few examples of how this can be achieved:

  • Lower Costs. As expected excess returns go down, the proportion taken by fees goes up.  The market may bear a 1% fee when expected excess returns are abundant, but that same fee may be the difference between retirement success and failure in a low return environment.  Therefore, the most obvious way to increase efficiency for investors is to lower costs: both explicit (fees) and implicit (trading costs and taxes).  Vanguard has led the charge in this arena for decades, and active managers are now scrambling to keep up.  While simply lowering fees is the most obvious solution, more creative fee arrangements (e.g. flexible fees) may also be part of the solution.
  • Increased Exposure to Active Views. In a recent commentary, It’s Long/Short Portfolios All the Way Down[3], we explored the idea that an active investment strategy is simply a benchmark plus a dollar-neutral long/short portfolio layered on top.  This framework implies that if the cost of accessing beta goes down, the implied cost for active necessarily goes up, creating a higher hurdle rate for active managers to clear.  In our perspective, the way to clear this hurdle is for active managers to offer portfolios with greater exposure to their active views, with the most obvious example being be a high active share / active risk, concentrated equity portfolio.  Such an approach increases the efficiency of exposure to active strategies.
  • Risk Management. Traditional risk management focuses exclusively on the use of capital diversification.  Traditionally allocated portfolios, however, are often significantly dominated by equity volatility and can therefore carry around a disproportionate amount of fixed income exposure to hedge against rare tail events.  We believe that diversifying your diversifiers – e.g. the incorporation of trend-following approaches – can potentially allow investors to increase their allocation to asset classes with higher expected returns without significantly increasing their risk profile.
  • Leverage.  As we saw in our example above, leverage may allow us to invest in more risk-efficient, diversified portfolios without necessarily sacrificing return.  In fact, in certain circumstances, it can even increase return.  So long as we can manage the risk, increasing notional exposure to $1.50 for every $1 invested in a low return environment is effectively like increasing our returns by 1.5x (less the cost of leverage).  For active strategies, a subtler example may be the return to a 130/30 style investment strategy (130% long / 30% short), which can allow investors enhanced access to a manager’s active views without necessarily taking on more beta risk.  We expect that institutional investors may begin to re-acquaint themselves with ideas like portable alpha, where traditional portfolio exposures may be used as collateral for market-neutral, alpha-seeking exposures.[4]

Portable Beta Theory

We see lower costs as inevitable: Vanguard has made sure of that.  We see increased exposure to active views as the only way for traditional active management (i.e. long-only stock pickers) to survive.  A number of alternative diversifiers have already made their way to market, including defensive factor tilts, long/flat trend-following, options strategies, and managed futures.  Leverage is where we really think new innovation can happen, because it allows investors to re-use­ capital to invest where they might not otherwise do so because it would have reduced their risk profile.

For example, for young investors the advice today is largely to invest predominately in equities and manage risk through their extended investment horizon.  This has worked historically in the United States, but there are plenty of examples where such a plan would have failed in other markets around the globe.  In truth, in almost no circumstance is 100% equities a prudent plan when leverage is available.[5]

As a simple example, let us constrain ourselves to only investing in stocks and bonds.  Using J.P. Morgan’s 2018 capital market assumption outlook[6], we can create a stock-bond efficient frontier.  In these assumptions, U.S. large-cap equities have an expected excess return of 4.4% with a volatility of 14.0%, while U.S. aggregate bonds have an expected excess return of 1.3% with a volatility of 3.8%.  The correlation between the two asset classes is zero.

Plotting the efficient frontier, we can also solve for the portfolio that maximizes the risk-adjusted expected excess return (“Sharpe optimal”).  We find that this mixture is almost exactly a 20% stock / 80% bond portfolio: a highly conservative mixture.  However, this mix has an expected excess return of just 1.92%.

Source: J.P. Morgan.  Calculations by Newfound Research.

However, if we are willing to apply 3.4-times leverage to this portfolio, so as to match the volatility profile of equities, the story changes.  A levered maximum Sharpe ratio portfolio – 278% bonds and 66% stocks – would now offer an expected excess return of 6.6%: a full 2.2% higher than a 100% stock portfolio (again ignoring the spread charged above the risk-free rate in real world for accessing leverage).

What if an investor already has a 100% equity portfolio with significant capital gains?  One answer would be to overlay the existing position with the exposure required to move the portfolio from its currently sub-optimal position to the optimal allocation.  In this case, we could sell-short a 34% notional position in the S&P 500, use the proceeds to buy 34% in a core U.S. bond position, and then borrow to buy the remaining 244%.  We would consider the -34% equity and +278% position in bonds our “portable beta.”

 

Original PortfolioTarget PortfolioPortable Beta
U.S. Equities100%66%-34%
U.S. Aggregate Bonds0%278%+278%

 

Portable Beta in Practice: Risk Cannot Be Destroyed, Only Transformed

In theory, the optimal decision is to lever a 20/80 stock/bond mix by 340%.  In practice, however, volatility is not an all-encompassing risk metric.  We know that moving from a portfolio dominated by equities to one dominated by bonds introduces significant sensitivity to interest rates.  Furthermore, the introduction of leverage introduces borrowing costs and operational risks that are not insignificant.

Risk parity proponents would argue that this is actually a beneficial shift, creating a more diversified profile to different risk factors.  In our example above, however, we can compare the results of a 100% stock portfolio to a 66% bond / 278% stock portfolio during the 1970s, when not only did interest rates climb precipitously, but the yield curve inverted (and remained inverted) on several occasions.

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities and a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index.  The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously.

While $1 invested on 12/31/1969 U.S. equities was worth $2.29 on 12/31/1981, the same dollar was worth only $0.87 in the levered portfolio.  Of course, the outlook for stocks and bonds (including expected excess return, volatility, and correlation) was likely sufficiently different in 1969 that the Sharpe optimal portfolio may not have been a 20/80.  Regardless, this highlights the significant gap between theory and practice.  In modern portfolio theory, capital market assumptions are assumed to be known ex-ante and asset returns are assumed to be normally distributed, allowing correlation to fully capture the relationship between asset classes.  In practice, capital market assumptions are a guess at best and empirical asset class returns exhibit fat-tails and non-linear relationships.

In this case in particular, an inverted yield curve can lead to negative expected excess returns for U.S. fixed income, correlation changes can lead to dramatic jumps in portfolio volatility, and the introduction of duration can lead to losses in a rising rate environment.  Thus, a large, concentrated, and static portable beta position may not be prudent.

Traditional portfolio theory tells us that an asset should only be added to a portfolio (though, the quantity not specified) if its Sharpe ratio exceeds the Sharpe ratio of the existing portfolio times the correlation of that asset and the portfolio.  We can use this rule to try to introduce a simple timing system to help manage risk.

When the trigger says to include bonds, we will invest in the Levered 20/80 portfolio; when the trigger says that bonds will be reductive, we will simply hold U.S. equities (labeled “Dynamic Levered 20/80” below).  We can see the results below:

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities, a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index.  The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously. 

Tactical timing, of course, introduces its own risks (including estimation risk, model risk, whipsaw risk, trading cost risk, reduced diversification risk, et cetera).  Regardless, empirical evidence suggests that styles like value, momentum, and carry may have power in forecasting the level and slope of the yield curve.[7]  That said, expanding the portable beta palette to include more asset classes (through explicit borrowing or derivatives contracts) may reduce the need for timing in preference of structural diversification.  Again, risk parity argues for exactly this.

In practice, few investors may be comfortable with notional leverage exceeding hundreds of percentage points.  Nevertheless, even introducing a modest amount of portable beta may have significant benefits, particularly for investors lacking in diversification.

For example, equity heavy investors may add little risk by introducing modest amounts of exposure to U.S. Treasuries.  Doing so may allow them to harvest the term premium over time and potentially even benefit from flight-to-safety characteristics that may offset equity losses in a crisis.  On a forward-looking basis (again, using J.P. Morgan’s 2018 capital market assumptions), we can see that using leverage to exposure to intermediate-term U.S. Treasuries is expected to both enhance return and reduce risk relative to a 100% equity portfolio.

Source: J.P. Morgan.  Calculations by Newfound Research.

How would this more moderate approach have fared historically? Below we plot the returns of U.S. equities, a constant 100/50 portfolio (a 100% equity / 50% bond portfolio achieved using leverage), a dynamic 100/50 portfolio (100% equity portfolio that selectively adds a levered 50% bond position using the same timing rules discussed above).

Ann. ReturnAnn. VolatilityMax Drawdown
U.S. Equities10.0%15.7%54.7%
100/50 Portfolio10.7%16.3%51.1%
Dynamic 100/50 Portfolio11.1%15.8%50.8%

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Constant 100/50 portfolio is comprised of a 100% position in U.S. equities and a 50% position in a 10-year constant maturity U.S. Treasury index funded by a -50% position in a constant maturity 1-year U.S. Treasury index.  The Dynamic 100/50 portfolio invests in either the U.S. Equity portfolio or the Constant 150/50 portfolio depending on the dynamic trade signal (see above).  The period of 2/1962 to 10/2017 represents the full set of available data.

We can see that the Dynamic 100/50 strategy is able to add 110 bps in annualized return with only an added 10 bps in increased volatility, while reducing the maximum realized drawdown by 390 bps.  Even naïve constant exposure to the Treasury position proved additive over the period.  Indeed, by limiting exposure, the Constant 100/50 portfolio achieved a positive 95.7% total return during the 1969-1981 period versus the -13% return we saw earlier.  While this still underperformed the 129.7% and 136.6% total returns achieved by U.S. equities and the Dynamic 100/50 portfolio respectively, it was able to add value compared to U.S. equities alone in 67% of years between 1981 and 2017.  For comparison, the Dynamic 100/50 strategy only achieved a 60% hit rate.

Conclusion

We will be the first to admit that these ideas are neither novel nor unique.  Indeed, the idea of portable beta is simply to take the theoretically inefficient exposure most investors hold and move it in the direction of a more theoretically optimal allocation through the prudent use of leverage.  Of course, the gap between theory and practice is quite large, and defining exactly what the optimal target portfolio actually is can be quite complicated.

While the explicit concept of portable beta may be more palatable for institutions, we believe the concepts can, and should, find their way into packaged format.  We believe investors can benefit from building blocks that enable the use of leverage and therefore allow for the construction of more risk- and capital-efficient portfolios.  Indeed, some of these ideas already exist in the market today.  For example:

  • Risk parity portfolios.
  • An alpha-generating fixed-income portfolio overlaid with equity futures.
  • The S&P 500 overlaid with a position in gold futures.
  • A strategic 60/40 allocation overlaid with a managed futures strategy.

We should consider, at the very least, how packed leverage applied to our traditional asset class exposures may allow us to free up capital to invest in other diversifying or alpha-seeking opportunities.  The 100/50 portfolio discussed before is, effectively, a 66/34 portfolio levered 1.5 times.  Thus, putting 2/3rds of our capital in the 100/50 portfolio gives us nearly the same notional exposure as a 60/40, effectively freeing up 1/3rd of our capital for other opportunities.  (Indeed, with some mental accounting gymnastics, we can actually consider it to be the same as holding a 66/34 portfolio with 100% of our capital and using leverage to invest elsewhere.)

While “no derivatives, leverage, or shorting” may have been the post-2008 mantra for many firms, we believe the re-introduction of these concepts may allow investors to achieve much more risk-efficient investment portfolios.

 

 

[1] https://www.barrons.com/articles/whats-next-for-etfs-1510976833

[2] Scylla and Charybdis were monsters in Greek mythology.  In The Odyssey, Odysseus was forced to sail through the Strait of Messina, where the two monsters presided on either side, posing an inescapable threat.  To cross, one had to be confronted.  The equivalent English seafaring phrase is, “Between a rock and a hard place.”

[3] https://blog.thinknewfound.com/2017/11/longshort-portfolios-all-the-way-down/

[4] https://en.wikipedia.org/wiki/Portable_alpha

[5] https://www.aqr.com/library/journal-articles/why-not–equities

[6] https://am.jpmorgan.com/us/institutional/our-thinking/2018-long-term-capital-market-assumptions

[7] See Duration Timing with Style Premia (Newfound 2017) and Yield Curve Premia (Brooks and Moskowitz 2017)

 

Addressing Low Return Forecasts in Retirement with Tactical Allocation

By

On September 25, 2017

In Risk Management, Sequence Risk, Weekly Commentary

This post is available for download as a PDF here.

Summary­­

  • The current return expectations for core U.S. equities and bonds paint a grim picture for the success of the 4% rule in retirement portfolios.
  • While varying the allocation to equities throughout the retirement horizon can provide better results, employing tactical strategies to systematically allocate to equities can more effectively reduce the risk that the sequence of market returns is unfavorable to a portfolio.
  • When a tactical strategy is combined with other incremental planning and portfolio improvements, such as prudent diversification, more accurate spending assessments, tax efficient asset location, and fee-conscious investing, a modest allocation can greatly boost likely retirement success and comfort.

Over the past few weeks, we have written a number of posts on retirement withdrawal planning.

The first was about the potential impact that high core asset valuations – and the associated muted forward return expectations – may have on retirement.

The second was about the surprisingly large impact that small changes in assumptions can have on retirement success, akin to the Butterfly Effect in chaos theory. Retirement portfolios can be very sensitive to assumed long-term average returns and assumptions about how a retiree’s spending will evolve over time.

In the first post, we presented a visualization like the following:

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation
Source: Shiller Data Library.  Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

The horizontal (x-axis) represents the year when retirement starts.  The vertical (y-axis) represents the years post-retirement.  The coloring of each cell represents the savings balance at a given point in time.  The meaning of each color as follows:

  • Green: Current account value greater than or equal to initial account value (e.g. an investor starting retirement with $1,000,000 has a current account balance that is at least $1,000,000).
  • Yellow: Current account value is between 75% and 100% of initial account value
  • Orange: Current account value is between 50% and 75% of the initial account value.
  • Red: Current account value is between 25% and 50% of the initial account value.
  • Dark Red: Current account value is between 0% and 25% of initial account value.
  • Black: Current account value is zero; the investor has run out of money.

We then recreated the visualization, but with one key modification: we adjusted the historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations[1] given current valuation levels.  We did this by subtracting the difference between the actual average log return and the forward-looking long return from each year’s return.  With this technique, we capture the effect of subdued average returns while retaining realistic behavior for shorter-term returns.

 

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation with Current Return Expectations

Source: Shiller Data Library.  Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

One downside of the above visualizations is that they only consider one withdrawal rate / portfolio composition combination.  If we want the see results for withdrawal rates ranging from 1% to 10% in 1% increments and portfolio combinations ranging from 0/100 stocks/bonds to 100/0 stocks/bonds in 20% increments, we would need sixty graphs!

To distill things a bit more, we looked at the historical “success” of various investment and withdrawal strategies.  We evaluated success on three metrics:

  1. Absolute Success Rate (“ASR”): The historical probability that an individual or couple will not run out of money before their retirement horizon ends.
  2. Comfortable Success Rate (“CSR”): The historical probability that an individual or couple will have at least the same amount of money, in real terms, at the end of their retirement horizon compared to what they started with.
  3. Ulcer Index (“UI”): The average pain of the wealth path over the retirement horizon where pain is measured as the severity and duration of wealth drawdowns relative to starting wealth. [2]

As a quick refresher, below we present the ASR for various withdrawal rate / risk profile combinations over a 30-year retirement horizon first using historical returns and then using historical returns adjusted to reflect current valuation levels.  The CSR and Ulcer Index table illustrated similar effects.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. Horizon

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon

Source: Shiller Data Library.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Overall, our analysis suggested that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip.

The combined conclusion of these two posts is that the near future looks pretty grim for retirees and that an assumption that is slightly off can make the outcome even worse.

Now, we are going to explore a topic that can both mitigate low growth expectations and adapt a retirement portfolio to reduce the risk of a bad planning assumption. But first, some history.

 

How the 4% Rule Started

In 1994, Larry Bierwirth proposed the 4% rule, and William Bengen expanded on the research in the same year.[3], [4]

In the original research, the 4% rule was derived assuming that the investor held a 50/50 stock/bond portfolio, rebalanced annually, withdrew a certain percentage of the initial balance, and increased withdrawals in line with inflation. 4% is the highest percentage that could be withdrawn without ever running out of money over an historical 30-year retirement horizon.

Graphically, the 4% rule is the minimum value shown below.

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon

Source: Shiller Data Library.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Since its publication, the rule has become common knowledge to nearly all people in the field of finance and many people outside it. While it is a good rule-of-thumb and starting point for retirement analysis, we have two major issues with its broad application:

  1. It assumes that not running out of money is the only goal in retirement without considering implications of ending surpluses, return paths that differ from historical values, or evolving spending needs.
  2. It provides a false sense of security: just because 4% withdrawals never ran out of money in the past, that is not a 100% guarantee that they won’t in the future.

 

For example, if we adjust the stock and bond historical returns using the estimates from Research Affiliates (discussed previously) and replicate the analysis Bengen-style, the safe withdrawal rate is a paltry 2.6%.

 

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon using Current Return Estimates

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

While this paints a grim picture for retirement planning, it’s not likely how one would plan their financial future. If you were to base your retirement planning solely on this figure, you would have to save 54% more for retirement to generate the same amount of annual income as with the 4% rule, holding everything else constant.

In reality, even with the low estimates of forward returns, many of the scenarios had safe withdrawal rates closer to 4%. By putting a multi-faceted plan in place to reduce the risk of the “bad” scenarios, investors can hope for the best while still planning for the worst.

One aspect of a retirement plan can be a time-varying asset allocation scheme.

 

Temporal Risk in Retirement

Conventional wisdom says that equity risk should be reduced as one progresses through retirement. This is what is employed in many “through”-type target date funds that adjust equity exposure beyond the retirement age.

If we heed the “own your age in bonds” rule, then a retiree would decrease their equity exposure from 35% at age 65 to 5% at the end of a 30-year plan horizon.

Unfortunately, this thinking is flawed.

When a newly-minted retiree begins retirement, their success is highly dependent on their first few years of returns because that is when their account values are the largest. As they make withdrawals and are reducing their account values, the impact of a large drawdown in dollar terms is not nearly as large.  This is known as sequence risk.

As a simple example, consider three portfolio paths:

  • Portfolio A: -30% return in Year 1 and 6% returns for every year from Year 2 – Year 30.
  • Portfolio B: 6% returns for every year except for Year 15, in which there is a -30% return.
  • Portfolio C: 6% returns for every year from Year 1 – Year 29 and a -30% return in Year 30.

These returns work about to the expected returns on a 60/40 portfolio using Research Affiliates’ Yield & Growth expectations, and the drawdown is approximately in line with the drawdown on a 60/40 portfolio over the past decade.  We will assume 4% annual withdrawals and 2% annual inflation with the withdrawals indexed to inflation.

 

3 Portfolios with Identical Annualized Returns that Occur in Different Orders

Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with. Portfolio B makes it through, not as comfortably as Portfolio C but still with 61% of its starting wealth. Portfolio A, however, starts off stressful for the retiree and runs out of money in year 27.

Sequence risk is a big issue that retirement portfolios face, so how does one combat it with dynamic allocations?

 

The Rising Glide Path in Retirement

Kitces and Pfau (2012) proposed the rising glide path in retirement as a method to reduce sequence risk.[5]  They argued that since retirement portfolios are most exposed to market risk at the beginning of the retirement period, they should start with the lowest equity risk and ramp up as retirement progresses.

Based on Monte Carlo simulations using both capital market assumptions in line with historical values and reduced return assumptions for the current environment, the paper showed that investors can maximize their success rate and minimize their shortfall in bad (5th percentile) scenarios by starting with equity allocations of between 20% and 40% and increasing to 60% to 80% equity allocations through retirement.

We can replicate their analysis using the reduced historical return data, using the same metrics from before (ASR, CSR, and the Ulcer Index) to measure success, comfort, and stress, respectively.

 

Absolute Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Note that the main diagonal in the chart represents static allocations, above the main diagonal represents the decreasing glide paths, and below the main diagonal represents increasing glide paths.

Since these returns are derived from the historical returns for stocks and bonds (again, accounting for a depressed forward outlook), they capture both the sequence of returns and shifting correlations between stocks and bonds better than Monte Carlo simulation. On the other hand, the sample size is limited, i.e. we only have about 4 non-overlapping 30 year periods.

Nevertheless, these data show that there was not a huge benefit or detriment to using either an increasing or decreasing equity glide path in retirement based on these metrics. If we instead look at minimizing expected shortfall in the bottom 10% of scenarios, similar to Kitces and Pfau, we find that a glide path starting at 40% rising to around 80% performs the best.

However, it will still be tough to rest easy with a plan that has an ASR of around 60 and a CSR of around 30 and an expected shortfall of 10 years of income.

With these unconvincing results, what can investors do to improve their retirement outcomes through prudent asset allocation?

 

Beyond a Static Glide Path

There is no reason to constrain portfolios to static glide paths. We have said before that the risk of a static allocation varies considerably over time. Simply dictating an equity allocation based on your age does not always make sense regardless of whether that allocation is increasing or decreasing.

If the market has a large drawdown, an investor should want to avoid this regardless of where they are in the retirement journey. Missing drawdowns is always beneficial as long as enough upside is subsequently realized.

In recent papers, Clare et al. (2017 and 2017) showed that trend following can boost safe withdrawal rates in retirement portfolios by managing sequence risk. [6],[7]

The million-dollar question is, “how tactical should we be?”

The following charts show the ASR, CSR, and Ulcer index values for static allocations to stocks, bonds, and a simple tactical strategy that invests in stocks when they are above their 10-month simple moving average (SMA) and in bonds otherwise.

The charts are organized by the minimum and maximum equity exposures along the rows and columns. The charts are symmetric across the main diagonal so that they can be compared to both increasing and decreasing equity glide paths.

The equity allocation is the minimum of the row and column headings, the tactical strategy allocation is the absolute difference between the headings, and the bond allocation is what’s needed to bring the total allocation to 100%.

For example, the 20% and 50% column is a portfolio of 20% equities, 30% tactical strategy, and 50% bonds. It has an ASR of 75, a CSR of 40, and an Ulcer index of 22.

 

Absolute Success Rate for Various Tactical Allocation Bounds Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

These charts show that being tactical is extremely beneficial under these muted return expectations and that being highly tactical is even better than being moderately tactical.

So, what’s stopping us from going whole hog with the 100% tactical portfolio?

Well, this is a case where a tactical strategy can reduce the risk of not making it through the 30-year retirement at the risk of greatly increasing the ending wealth. It may sound counterintuitive to say that ending with too much extra money is a risk, but when our goal is to make it through retirement comfortably, taking undue risks come at a cost.

For instance, we know that while the tactical strategy may perform well over a 30-year time horizon, it can go through periods of significant underperformance in the short-term, which can lead to stress and questioning of the investment plan. For example, in 1939 and 1940, the tactical strategy underperformed a 50/50 portfolio by 16% and 11%, respectively.

These times can be trying for investors, especially those who check their portfolios frequently.[8] Even the best-laid plan is not worth much if it cannot be adhered to.

Being tactical enough to manage the risk of having to make a major adjustment in retirement while keeping whipsaw, tracking error, and the cost of surpluses in check is key.

 

Sizing a Tactical Sleeve

If the goal is having the smallest tactical sleeve to boost the ASR and CSR and reduce the Ulcer index to acceptable levels in a low expected return environment, we can turn back to the expected shortfall in the bad (10th percentile) scenarios to determine how large of a tactical sleeve to should include in the portfolio. The analysis in the previous section showed that being tactical could yield ASRs and CSRs in the 80s and 90s (dark green).  This, however, requires a tactical sleeve between 50% and 70%, depending on the static equity allocation.

Thankfully, we do not have to put the entire burden on being tactical: we can diversify our approaches.  In the previous commentaries mentioned earlier, we covered a number of topics that can improve retirement results in a low expected return environment.

  • Thoroughly examine and define planning factors such as taxes and the evolution of spending throughout retirement.
  • Be strategic, not static: Have a thoughtful, forward-looking outlook when developing a strategic asset allocation. This means having a willingness to diversify U.S. stocks and bonds with the ever-expanding palette of complementary asset classes and strategies.
  • Utilize a hybrid active/passive approach for core exposures given the increasing availability of evidence-based, factor-driven investment strategies.
  • Be fee-conscious, not fee-centric. For many exposures (e.g. passive and long-only core stock and bond exposure), minimizing cost is certainly appropriate. However, do not let cost considerations preclude the consideration of strategies or asset classes that can bring unique return generating or risk mitigating characteristics to the portfolio.
  • Look beyond fixed income for risk management given low interest rates.
  • Recognize that the whole can be more than the sum of its parts by embracing not only asset class diversification, but also strategy/process diversification.

While each modification might only result in a small, incremental improvement in retirement outcomes, the compounding effect can be very beneficial.

The chart below shows the required tactical sleeve size needed to minimize shortfalls/surpluses for a given improvement in the annual returns (0bp through 150bps).

 

Tactical Allocation Strategy Size Needed to Minimize 10% Expected Shortfall/Surplus with Average Stock and Bond Returns Equal to Current Expectations for a Range of Annualized Return Improvements  – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

For a return improvement of 125bps per year over the current forecasts for static U.S. equity and bond portfolios, with a static equity allocation of 50%, including a tactical sleeve of 20% would minimize the shortfall/surplus.

This portfolio essentially pivots around a static 60/40 portfolio, and we can compare the two, giving the same 125bps bonus to the returns for the static 60/40 portfolio.

 

Comparison of a Tactical Allocation Enhanced Portfolio with a Static 60/40 Portfolio with Average Stock and Bond Returns Equal to Current Expectations + 125bps per year   – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

In addition to the much more favorable statistics, the tactically enhanced portfolio only has a downside tracking error of 1.1% to the static 60/40 portfolio.

 

Conclusion: Being Dynamic in Retirement

From this historical analysis, high valuations of core assets in the U.S. suggest a grim outlook for the 4% rule. Predetermined dynamic allocation paths through retirement can help somewhat, but merely specifying an equity allocation based on one’s age loses sight of the changing risk a given market environment.

The sequence of market returns can have a large impact on retirement portfolios. If a drawdown happens early in retirement, subsequent returns may not be enough to provide the tailwind that they have in the past.

Investors who are able to be fee/expense/tax-conscious and adhere to prudent diversification may be able to incrementally improve their retirement outlook to the point where a modest allocation to a sleeve of tactical investment strategies can get their portfolio back to a comfortable success rate.

Striking a balance between shortfall/surplus risk and the expected experience during the retirement period along with a thorough assessment of risk tolerance in terms of maximum and minimum equity exposure can help dictate how flexible a portfolio should be.

In our QuBe Model Portfolios, we pair allocations to tactically managed solutions with systematic, factor based strategies to implement these ideas.

While long-term capital market assumptions are a valuable input in an investment process, adapting to shorter-term market movements to reduce sequence risk may be a crucial way to combat market environments where the low return expectations come to fruition.

[1] Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates.  These capital market assumptions assume that there is no valuation mean reversion (i.e. valuations stay the same going forward).  The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.1%, respectively, compared to the historical values of 9.0% and 5.3%.

[2] Normally, the Ulcer Index would be measured using true drawdown from peak, however, we believe that using starting wealth as the reference point may lead to a more accurate gauge of pain.

[3] Bierwirth, Larry. 1994. Investing for Retirement: Using the Past to Model the Future. Journal of Financial Planning, Vol. 7, no. 1 (January): 14-24.

[4] Bengen, William P. 1994. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning, vol. 7, no. 4 (October): 171-180.

[5] Pfau, Wade D. and Kitces, Michael E., Reducing Retirement Risk with a Rising Equity Glide-Path (September 12, 2013). Available at SSRN: https://ssrn.com/abstract=2324930

[6] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017). Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Available at SSRN: https://ssrn.com/abstract=3019089

[7] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017) Reducing Sequence Risk Using Trend Following and the CAPE Ratio. Financial Analysts Journal, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2764933

[8] https://blog.thinknewfound.com/2017/03/visualizing-anxiety-active-strategies/

Building an Unconstrained Sleeve

By

On July 31, 2017

In Portfolio Construction, Risk Management, Weekly Commentary

We’re often asked about how to build an unconstrained sleeve in a portfolio.

Our view is that your mileage will largely vary by where you are trying to go.  With that in mind, we focus on three objectives:

  • Sleeves that seek to hedge equity losses.
  • Sleeves that seek significant equity upside capture while reducing downside.
  • Sleeves that seek an absolute return profile.

We explore how these sleeves can be built using common strategies such as tactical equity, minimum volatility equity, managed futures, risk parity, global contrarian, alternative income, and traditional U.S. Treasuries.

You can find the full presentation below.

 

(If the above slideshow is not working, you can view an online version here or download a PDF version here.)

 

Math Tests, Birthdays, O.J. Simpson, and Texas Sharpshooters

By

On June 20, 2016

In Risk Management, Weekly Commentary

This blog post is available as a PDF here.

Summary

  • Humans are not terribly good at accurately assessing probability and dealing with randomness.  This may stem from these skills having little evolutionary value.
     
  • We exhibit hindsight and confirmation bias.  We weave narratives around completely random events.  We assess probabilities using the wrong context.
     
  • These biases make performance evaluation difficult since security, asset class, and strategy returns have a random component.
     
  • Appreciating the role of randomness in portfolio results may quell some of the constant disappointment with diversification.  

Humans are generally really, really bad at dealing with randomness and probability.  In a 2008 article, Michael Shermer labeled this difficulty “folk numeracy.”  He described “folk numeracy” as follows:

“Folk numeracy is our natural tendency to misperceive and miscalculate probabilities, to think anecdotally instead of statistically, and to focus on and remember short-term trends and small-number runs.  We notice a short stretch of cool days and ignore the long-term global-warming trend.  We note the consternation with the recent downturn in the housing and stock markets, forgetting the half-century upward-pointing trend line.  Sawtooth data trend lines, in fact, are exemplary of folk numeracy: our senses are geared to focus on each tooth’s up or down angle, whereas the overall direction of the blade is nearly invisible to us.”

From an evolutionary perspective, none of this should be too surprising.  Consider a person living in a jungle full of dangerous predators.  He hears a rustle behind him.  Is there any value in calculating the probability that the rustle was caused by a dangerous predator?  Of course there isn’t.  The cost of a false positive – fleeing a harmless situation – is tiny compared to the cost of a false negative – staying put since the odds are the situation is benign, only to be killed by a tiger.   

As Shermer’s article points out, our problems with probability are multi-faceted.  Below, we’ll discuss a few of the main issues. 

 

Narratives

Humans tend to weave narratives around the events they experience, even if those events are the result of pure randomness. 

Consider a high school math student.  After studying diligently for a ten-question test, she has a firm grasp on 90% of the material.  On average, this means that she should be an A student.  However, luck will play a pretty big role in her success or failure.  She will do better when the questions selected by the teacher overlap closely with her knowledge and worse when they do not.  

The probability of a C or lower is 7.0%.  While this outcome would be unlucky for someone that knows 90% of the material, we see that it certainly is not out of the question.

Test Probability Distribution

Say the student does indeed get a C.  Everyone involved is likely to start to weave a narrative to explain the disappointing grade.  The student might start to lose confidence, worrying that she was not as prepared as she thought.  The parents might think the student is slacking in her studies or distracted by friends or extracurricular activities.  She might get scolded, grounded, or forced to go to a tutor.  All of this storytelling occurs despite the fact that the score was nothing more than a bit a bad luck. 

 

Context

In other instances, humans get half of the way there.  They stop to consider probabilities and the role of randomness, but because they use the wrong context they still end up far from the mark. 

The Birthday Paradox is a prime example of this.  Say that you are in a room with 22 other individuals and are asked to estimate the probability that at least two people in the room share the same birthday. 

Posed with this question, most people guess that the probability is quite low.  In fact, the true probability of at least two people sharing a birthday is 50.7%.  Why?  Incorrect context. 

Birthday Paradox

The actual question posed was: What is the probability that at least two people in the room share the same birthday?

However, most people answer a slightly different question: What is the probability that someone in the room shares a birthday with me? 

The answer to this second question is quite low at 5.9%.  Most people get the right answer to the wrong question.  Their context is off. 

Another interesting example of incorrect context occurred during the O.J. Simpson trial, which has been in the spotlight recently thanks to two recent television series. 

A key aspect of the trial involved past domestic violence perpetrated by Simpson against Nicole Brown.  One of Simpson’s defense attorneys, Alan Dershowitz, argued against the relevance of this evidence by saying that fewer than 1 in 2,500 abusers go on to murder their spouses. 

Dershowitz wasn’t necessarily incorrect, but he provided the jury with the wrong context (which, perhaps, was his intention, given that he was defending Simpson).  In probability terms, he claims that the probability that a man murders his wife given that he abused her in the past is less than 1 in 2,500.

But this ignores the key fact that someone did in fact murder Brown.

The jury should be interested in a slightly different probability: the probability that a man murders his wife given that he abused her and that she has been murdered.  Using some additional data and a powerful tool called Bayes’ theorem, we find that this probability is actually around 89%.  89% may not be high enough to convict by itself, but would be powerful when combined with other evidence of guilt. 

 

Hindsight Bias and Confirmation Bias

From Wikipedia:

“Hindsight bias is the inclination, after an event has occurred, to see the event as having been predictable, despite their having been little or no objective basis for predicting it.”

“Confirmation bias is the tendency to search for, interpret, favor, and recall information in a way that confirms one’s preexisting beliefs or hypotheses, while giving disproportionally less consideration to alternative possibilities. 

The Texas Sharpshooter Fallacy illustrates both of these biases. 

Consider a cowboy randomly shooting at the side of a barn.  This cowboy is a terrible shot and so bullet holes are randomly dispersed on the barn’s surface.  Inevitably, some clusters start to develop as the cowboy takes more and more shots.  The cowboy locates the densest clusters and draws bull’s-eyes around them.  In the future, the cowboy uses the barn as evidence of his sharpshooting prowess. 

Cowboy Painting Target 

The Texas Sharpshooter Fallacy is more than an entertaining story.  It’s pervasive in many walks of life.  Journalist David McRaney pointed out a number of examples in an article on the topic.  For example, he wrote:

“In World War II, Londoners took notice when bombing raids consistently missed certain neighborhoods.  People began to believe German spies lived in the spared buildings.  They didn’t.  Analysis afterwards by psychologists Daniel Kahneman and Amos Tversky showed the bombing strike patterns were random.”

 

Diversification Disappoints

So what in the world does any of this have to do with investing? 

A few weeks back we explained why diversification, often called the only free lunch on Wall Street, will always disappoint. 

In our opinion, much of this frustration stems from the probability-related issues discussed above.  Diversification is valuable precisely because the future is uncertain, which means it should be evaluated with probability and randomness in mind. 

As an example, consider an investor that spreads her capital equally among ten different mutual funds (labeled A through J).  Her performance, both on a position-by-position and aggregate basis, is summarized in the following periodic table of returns. 

Asset Return Table

These are random, simulated returns generated assuming that each Fund’s returns are independently and identically distributed normal random variables.

 

One of the first things the investor will probably notice is the performance of Fund J.  Fund J not only is the worst performing over the full period, but also has the dubious distinction of underperforming the overall portfolio in all five years.  As a result, Fund J detracted from portfolio performance each and every year.

The investor draws a bull’s-eye right on Fund J, just like the Texas Sharpshooter. 

Asset Return Table #2

These are random, simulated returns generated assuming that each Fund’s returns are independently and identically distributed normal random variables.

 

Then the investor thinks, “Wow, what are the odds that a Fund underperforms for five consecutive years?  Probably pretty low.”

And she isn’t wrong.  The probability of Fund J underperforming for five years in a row is only 3.125%.  However, her context is wrong, just like in the Birthday Paradox and O.J. Simpson examples.  The more relevant question is: “What is the probability that at least one of my ten funds underperforms for five straight years?”  Using some simplifying assumptions, the answer is around 28%, far from a rare event[1]. 

As a quick mathematical aside, it’s worth nothing this probability will actually increase as more funds are added to the portfolio.  More diversified portfolios have greater odds of having long-term underperformers.  With twenty funds, the probability increases to nearly 50% – equivalent to a coin flip.  With thirty funds, the probability is above 60% and so it’s actually more likely than not that we have at least one fund underperform for 5 years in a row.  

With this incorrect probability assessment in hand, the investor weaves a narrative as to why Fund J underperformed.  Maybe there was a change in portfolio manager or the Fund’s process is fundamentally broken.  Maybe the Fund is too big or too small.  This is no different than searching for explanations as to why your A-student got a C on a math test. 

To be clear, we are not suggesting that investors put their collective heads in the sand and chalk up all performance variation to randomness.  A diligent parent won’t ignore their children’s grades and a diligent investor won’t stop trying to understand the sources of outperformance and underperformance just because randomness and luck happen to play a significant role in results, especially when sample sizes are small. 

However, we do believe that the best investors appreciate the starring role that randomness plays in investment results.  Gaining this appreciation may soothe some of the constant disappointment with diversification. 

 

[1] We assume that each fund’s annual return is independently and identically normal random variables and that there is no serial correlation from year to year.  We use these assumptions for all of the hypothetical portfolio analysis.

The State of Risk Management

By

On May 18, 2016

In Risk Management

How effective is your method of managing portfolio risk? We compare and contrast different approaches – including fixed income, managed futures, low volatility equities, and tactical – to explore the relative protection they can deliver versus the return drag they can create.

Page 10 of 11

Previous

Next

Powered by WordPress & Theme by Anders Norén