*This commentary is available here as a PDF. *

# Summary

- The “rules of the game” are crucial in investing. Specifically, care should be taken to ensure that the rules used in portfolio construction align with client expectations.

- Anecdotally, we see two situations where these rules differ. First, performance is often evaluated over time horizons that are much too short to be meaningful. Second, tracking error to popular indices, like the S&P 500, is sometimes used in evaluating the performance of globally diversified portfolios.

- The benefits of diversification can take extended periods of time to percolate into portfolio returns.

- Diversification depends on finding asset classes with diverse behavior. Tracking error constraints limit the ability to take advantage of this behavior and so often require a trade-off between benchmark tracking and risk-adjusted performance.

With the Presidential primaries increasingly dominating the news cycle, we’ve found ourselves spending more and more time browsing FiveThirtyEight.com. For those unfamiliar with the site, FiveThirtyEight is a blog started by statistician and author Nate Silver. It gives a unique, quant-oriented take on politics, sports, science, economics, and pop culture.

On Monday, Silver published an entry tilted “Donald Trump Would Be Easy to Stop Under Democratic Rules.” Now before anyone stops reading, we promise that this is not going to be a political post.

Rather, we think the article makes a nice point that ties into what we’ve been hearing in recent conversations with advisors.

In the article, Silver compares the Republican delegate standings as of March 7, 2016 to hypothetical standings computed using the following three sets of alternative rules:

**Winner-Take-All Rules**: The candidate receiving the most votes in each state gets all of that state’s delegates.

**Democratic Rules**: Roughly 85%/15% split between what we will refer to as modified proportional and superdelegates. Under the modified proportional system, delegates are split proportionally among candidates receiving at least 15% of the vote. As an example, assume that candidates A, B, and C get 60%, 30%, and 10% of the vote, respectively. Under the modified proportional system, candidate A would get 2/3^{rds}of the delegates, candidate B would get 1/3^{rd}of the delegates, and candidate C would get no delegates. Superdelegates are party leaders and elected officials that are able to vote for whichever candidate they want, regardless of their state’s primary or caucus results.

**Uniform Republican Rules**: A single set of rules applied uniformly to each state in an effort to mimic the results of the actual Republican primary system. In a sense, you can think of this as a “weighted average” of the unique systems used in each state for Republican primaries and caucuses.

*Source: FiveThirtyEight.com*

While Trump would lead under all four scenarios, the implications for the remainder of the race would be vastly different.

Silver writes that under Democratic rules, “it would be hard for Trump to ever get a majority under these circumstances; he’d have to get at least 72% of the elected delegates from the remaining states, or he’d need help from superdelegates who might not be willing to provide it to him.” A contested convention would seem to be the highest probability outcome under this scenario.

Under Winner-Take-All rules, Silver believes that Trump, while still vulnerable to a surge by Cruz, “would be in good shape for the nomination.”

The moral of the story: the rules of the game are pretty darn important.

But what does any of this have to do with investing?

One thing we’ve been hearing consistently from advisors is that clients are getting frustrated with diversification of all shapes and sizes.

In the 1950s, Harry Markowitz set forth some pretty simple rules for building portfolios. He reasoned that investors should attempt to maximize return per unit of risk. While we can, and often will, quibble with Markowitz’s exact implementation, his overarching theme of risk-adjusted returns remains powerful and intuitive.

We have a theory that at least part of the frustration with diversification is that portfolios are being constructed with different “rules of the game” than those being used by clients to evaluate the performance of said portfolios.

Our anecdotal evidence suggests that the rules being used to evaluate performance differ from Markowitz in two ways:

- Performance is being evaluated over time horizons that are too short to extract meaningful conclusions.

- Overall portfolio risk – whether measured by volatility, drawdown, or some other measure – is not the only metric being used to put returns into context. Many investors also care about tracking error to popular benchmarks, most notably the S&P 500.

**Time Horizons and Expectations **

The time horizon used to evaluate the performance of a security, asset class, or strategy is crucial. It makes zero sense to evaluate the performance of a 10-year Treasury note over a 1-year period. Interest rate movements in year one will push the return above or below the initial yield of the note. But none of this volatility will change the fact that the investment’s 10-year annualized return will equal its starting yield.

Another way to visualize the importance of time is with a simple example. Let’s say that your portfolio currently has an expected excess return of 5% with 10% volatility.

A manager comes along saying he’s got a great strategy with 5% expected return and 20% volatility (note: this is a large-cap equity type of return profile). While the Sharpe ratio is only half that of your current portfolio (0.25 vs. 0.50), the strategy is compelling because it is completely uncorrelated with your existing holdings. Furthermore, let’s assume that you know all of this data to be exactly true. The yearly return for the manager is indeed normally distributed with a 5% mean, 20% standard deviation, and no correlation to your existing portfolio.

Mr. Markowitz would say the manager deserves a 20% allocation. Great, but how should we set client expectations for this new manager?

The graph below plots the probability that the manager’s average return will be negative over different time horizons. In the first year, there is a 40% probability that the manager will lose money. Over five years, there is still a 29% chance that the manager will be negative over the investment horizon.

In fact, the probability of a negative average annual return does not drop below 10% until we’ve stuck with the manager for 27 years! Imagine having to tell a client that you have a 20% allocation to a manager that has lost money over a 27-year period. While this would be an unlucky outcome at 10% probability, it is far from an outlier.

*Source: Newfound Research. Assumes returns from a normal distribution with mean of 5% and standard deviation of 20%.*

The reality of investing is that even asset classes or strategies that are solid long-term plays can underperform for protracted periods of time. Firing the manager (or removing the asset class) might feel good, but would be irrational.

**Tracking Error **

Diversification fundamentally relies upon finding investments that behave differently from one another. While investors may care about tracking error to an index like the S&P 500, it is important to understand the trade-offs associated with such an approach. (Note: Tracking error is a measure of how closely one portfolio or security follows another portfolio or security).

It’s worth noting that what clients *really* want is high, positive tracking error on the downside and zero tracking error on the upside. This is very, very hard to achieve with “linear” instruments (e.g. basic asset allocation). Either convex asset classes must be used (e.g. options), all of which come with their own downsides, or the portfolio must be dynamically adjusted over time.

A preference for low tracking error, if incorporated into portfolio construction, will anchor the portfolio’s allocations towards the benchmark, limiting the diversification that can be harvested via allocations to less than perfectly correlated investments.

A simple example can again help to illustrate our point. Suppose we have access to benchmark asset XYZ and an unlimited number of other assets that are uncorrelated to XYZ.

Below, we plot the portfolio’s Sharpe ratio and its tracking error to XYZ. As more assets are added to the portfolio, the Sharpe ratio increases as we take advantage of the “free lunch” of portfolio diversification. However, increasing the number of assets in the portfolio also increases tracking error to XYZ.

*Source: Newfound Research. Assumes returns from a normal distribution with mean of 5% and standard deviation of 20%.*

To make the example a little more concrete, we pulled ETF data for the following 13 asset classes:

- U.S. Large-Cap (SPY)
- U.S. Mid-Cap (IJH)
- U.S. Small-Cap (IJR)
- Foreign Developed Equity (EFA)
- Emerging Markets Equity (EEM)
- 1-3 Yr. Treasuries (SHY)
- 7-10 Yr. Treasuries (IEF)
- 20+ Yr. Treasuries (TLT)
- Barclays Aggregate Bond (AGG)
- High Yield (VWEHX)
- TIPs (TIP)
- Gold (GLD)
- REITs (VNQ)

Using return data for the shared history of these securities, which goes back to November 2004, we constructed what would have been the Sharpe optimal portfolio over this period. **Important note: we explicitly are using look ahead bias here by assuming we knew returns, volatilities, and correlations ahead of time. In practice, this is impossible. **

The Sharpe-optimal portfolio would have achieved very impressive results, but not without a whole lot of tracking error to SPY.

SPY | Sharpe-Optimal Portfolio | |

Annualized Return | 6.6% | 7.1% |

Annualized Volatility | 14.9% | 5.6% |

Maximum Drawdown | 50.8% | 8.5% |

Sharpe Ratio | 0.29 | 0.86 |

Tracking Error to SPY | 0.0% | 13.1% |

*Source: Data from Yahoo! Finance. Calculations by Newfound Research. Past performance does not guarantee future results. The results for the Sharpe-Optimal Portfolio are hypothetical and backtested returns that explicitly utilize look-ahead bias in their calculation. Results are not indicative of any Newfound index or strategy. Hypothetical performance results have many inherent limitations and are not indicative of results that any investor actually attained. An investor cannot invest directly in an index. Index returns are unmanaged and do not reflect any fees or expenses. Data is for the period from November 2004 to February 2016. Assumes the reinvestment of dividends and other distributions. *

The annual out/underperformance of the Sharpe-optimal portfolio vs. SPY does a good job of giving context to the magnitude of this tracking error.

*Source: Data from Yahoo! Finance. Calculations by Newfound Research. Past performance does not guarantee future results. The results for the Sharpe-Optimal Portfolio are hypothetical and backtested returns that explicitly utilize look-ahead bias in their calculation. Results are not indicative of any Newfound index or strategy. Hypothetical performance results have many inherent limitations and are not indicative of results that any investor actually attained. An investor cannot invest directly in an index. Index returns are unmanaged and do not reflect any fees or expenses. Data is for the period from November 2004 to February 2016. Assumes the reinvestment of dividends and other distributions. *

None of this should be too surprising since our Sharpe ratio is a *total period *measure, and captures *nothing *about intra-period volatility that may occur. See our “God, Buffett, and the Three Oenophiles” post for more in-depth discussion of this topic.

We can solve the tracking error problem by maximizing Sharpe ratio subject to a tracking error constraint. Predictably, the cost of lower tracking error is worse risk-adjusted performance.

*Source: Data from Yahoo! Finance. Calculations by Newfound Research. Past performance does not guarantee future results. The results for the Sharpe-Optimal Portfolio are hypothetical and backtested returns that explicitly utilize look-ahead bias in their calculation. Results are not indicative of any Newfound index or strategy. Hypothetical performance results have many inherent limitations and are not indicative of results that any investor actually attained. An investor cannot invest directly in an index. Index returns are unmanaged and do not reflect any fees or expenses. Data is for the period from November 2004 to February 2016. Assumes the reinvestment of dividends and other distributions. *

The tighter we make the tracking error constraint, the less the portfolio is able to take advantage of the diversifying benefits of bonds, REITs, and gold.

The rules of the game are vital in both politics and investing. Care should be taken that the rules used in portfolio construction coalesce with client objectives. Dissonance between these sets of rules is a recipe for frustration for all involved.

A large step towards protecting against this dissonance is to more deeply understand what diversification is and what it isn’t. Diversification is a statistical concept that assumes an infinite number of potential future paths. We will only end up realizing one of these possible futures. The exact future we end up in may make diversification a total drag or a total benefit. Diversification is important precisely because we do not know what the future holds. As a result, evaluating its worth with the benefit of hindsight, where there is no uncertainty, can be at best misleading and at worst downright dangerous.

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