You can download this blog post here.


  • Investors often focus their analysis on benefits.  In the finance industry, we’ve distilled this down to a single metric: alpha.
  • Benefits and risk require separate analysis.  Increasing benefits does not necessarily reduce risk or even leave it unchanged.
  • In practice, increasing alpha can actually increase risk in many portfolios.

We would like to tip our hats to N.N. Taleb, whose recent writings on the difference between benefits and risk inspired this commentary.

We think it is fair to make the sweeping generalization that investors are obsessed with outperforming the market.  Why?  Because of an even greater generalization: people are greedy.

Greed can make people myopically focus on potential rewards and neglect any added risk.  In the finance industry, we’ve gone so far as to distill this entire notion down to a single statistic: alpha.

In mathematical terms, the concept of alpha comes from an equation describing the returns of a stock, which looks something like:

To translate: “the return of a stock is equal to alpha () plus some broad market sensitivity () plus the risk-free rate () plus some company specific, idiosyncratic risk ().”

Now, theoretically  should be zero.  By construction, the  of the market must be zero.  If  is positive for one or more stocks, then it must be negative for other stocks.  Smart investors, recognizing this situation, will move away from market-cap weighting, selling the negative alpha stocks and buying the positive alpha ones, eventually driving  to zero.

For simplicity, assume that there is one stock with positive alpha (stock P) and one stock with negative alpha (stock N) and that both have .  Overweighting P vs. N is identical to holding the market portfolio and adding a long-short portfolio that is long P and short N to your portfolio.

The return of this long-short portfolio will be:

If the idiosyncratic risks are independent from one another, then over the long run they should diversify away each other and your expected return will increase by a factor of .  This increase is about as close as you can get to free money.  Unfortunately, other investors would flock to copy this approach, driving both alphas to zero.

The situation above is an oversimplification of the real world.  The reality is that alpha can be generated in the long-term, but not in the risk-free sense.  As we mentioned, in our ideal world the idiosyncratic risks diversify each other away over the long run.  In reality, they are often not independent and in the short-run, fiercely correlated.

Long-term alpha generation requires taking on short-term risk, either absolute (risk of ruin) or relative (risk of underperformance of a benchmark) risk.

Investors frequently just focus on maximizing alpha without considering risk.  But alpha is not a risk management policy – and often its pursuit causes an increase of risk.

Evidence from pricing insurance

A put option, a contract that protects the purchaser from losses greater than a certain level, is a form of financial insurance.  We can explore the relationship between benefits and risks by observing how the price of the put reacts to changes in the assumptions regarding expected return and volatility.

Before we continue, it’s important to make clear that we are distinguishing between downside risk and volatility.  Volatility can often be beneficial.  As an example, innovation is often quite volatile.  Downside risk, on the other hand, can actually lead to ruin.  There is little penalty for upside volatility, but often there is an absorption barrier on the downside that, when hit, leads to permanent ruin.

As an example, consider that stressing the human body can actually be quite good for it.  The right amount of physical exertion can lead to increased strength, cardiovascular stamina, and overall health.  Too much stress, however, can lead to significant injury.  The same goes for a company.  A little bit of innovation and volatility can be good.  Too much can drive it into permanent bankruptcy.

A portfolio of stocks may similarly benefit from increased volatility if it comes with a commensurate increase in expected return. Excessive losses due to increased volatility, however, can lead to permanent ruin.

By pricing how much it costs to protect ourselves against losses above a certain level (in this following examples we use -15%), we can more accurately understand how changing expected return and volatility levels actually affects our risk of ruin.

(Note: those more familiar with options may be scratching their head at this point because expected return should not come into play when pricing an option.  In Black Scholes, there is a spot to input the risk-free rate, but nowhere to place expected return.  This is true if we assume that the current market price is the best guess for the discounted future market price – i.e. price is a martingale.  In this case, we assume our view differs from that of the market, and hence the current market price is not correct.  So we use Monte Carlo simulation to price the option.)

First, we look at how the option price changes with expected return, holding volatility constant.


To read this chart, first identify the volatility level associated with a given curve.  Then we can see how the price changes (y-axis) for changes in expected return (x-axis).  For example, the top, dark blue curve corresponds to 19% volatility.  With a 1% expected return, the put-option costs $1.74.  At a 9% expected return, the put option costs $0.78.

We can see that the price of protection decreases as expected return goes up.  This shouldn’t be surprising since the higher the expected return, the rarer (higher sigma) a loss must be to hit a given level of loss.

That being said, the price decrease is not dramatic.  At the most volatile level – 19% – increasing expected return from 1% to 9% (a 900% increase!) only decreases the cost of protection from $1.74 to $0.78, a 55% reduction.

Now let’s hold expected return constant and vary volatility levels.

Put Price for Sigma

The impact is much more dramatic.  As we calculated before, the put option would cost $0.78 when expected return is 9% and volatility is 19%.  However, if we reduce the volatility to 11%, the option costs only $0.04.  That’s a 94.8% reduction in price.

So it is not entirely fair to say that alpha does not help us manage risk, increasing expected return does slightly reduce the cost of insurance.  However, changes in volatility can easily swamp expected return increases.

As an example of this, assume that expected return is 4% and volatility is 12%.  The put price is $0.21.  Now assume that expected return doubles to 8% and volatility increases by a much more modest 25% to 15%.  The put price is now $0.32, an increase of 52%.

What becomes clear is that increasing expected return does relatively little to decrease our risk of ruin.

Benefits come with their own variance: evidence from the value premium

In last week’s commentary, we discussed how active strategies should be an allocation and not a trade within client portfolios.  Our argument was based on the time-varying nature of active return premiums.

We found that while an approach like value investing can have a positive long-run expected relative return against the broader market, the premium comes with significant variation.

Our argument for why the premium must vary was simple: if it didn’t, it would be viewed as free, causing an inflow of capital, driving valuations up and forcing the premium towards zero.  In other words, for the premium to exist over the long run, it must be volatile enough in the short-run to not be viewed as “free” by investors.

To get a sense of how volatile this premium can be, we’ve plotted trailing 2-year excess returns of a value-tilt portfolio versus the broad market.

varying value premium

Source: Kenneth French Data Library.  Analysis by Newfound Research.

We can see that with a value approach, there are periods of feast (+57% in 1997; +53% in 2002) and famine (-23% in 1980; -40% in 2000).

An investor with the fortitude to stomach this relative volatility was handsomely rewarded by an excess annualized return of 3.24% a year.  This benefit, however, came at the cost of a higher annualized volatility and a larger maximum drawdown.

Expected ReturnVolatilityMax Drawdown
Value Tilt13.20%16.67%-59.22%
Source: Kenneth French Data Library.  Analysis by Newfound Research. 

As we mentioned in the first section, diversification across large number of stocks should just leave us with a constant alpha term.  Yet in the graph above we can see that buying a large number of value stocks and shorting the market is highly volatile.  What gives?

While the answer is multi-faceted, one prominent reason is that the stocks all share a common risk characteristic: value. The whole idea was that the idiosyncratic volatility was company specific, and therefore independent between stocks.  However, in this case, there is a common, shared risk characteristic that cannot be diversified away.

We believe there are two important takeaways here:

  • Using a theoretical option-pricing framework, we’ve shown that volatility is a much more important component to the risk-of-ruin than expected return.
  • Using the example of factor investing, we’ve noted that sources of alpha often come with their own volatility, and that increasing long-term expected return can also increase short-term potential for loss.  Performance chasers, who have difficulty sticking to a single approach, are likely to experience repeated episodes of relative underperformance (e.g. 1980 and 2000 with value) without ever seeing the upside because they’ve already jumped ship to another methodology.  They’ve folded, forfeiting alpha to those with the guts to hold.  Do this enough times, and the amount of underperformance can be devastating to long-term growth even during periods of strong broad-market equity performance.

Investors focused on only maximizing the return side of the equation may not always be aware of the extra risks they are taking on in chasing that return.  In an industry where benefit is distilled down to a single number – alpha – it is important to remember the return and risk require separate analysis.