The Blunt Ratio (Part 2)
Investors can’t eat Sharpe ratios. Following historical drawdowns, some investors may have starved to death by holding “stable” stocks that were too slow to bounce back.
By: Verdad Research
Last week we covered a hypothetical example of Nassim Taleb’s argument against using standard deviation as a measure of risk and Sharpe ratio as a measure of risk-adjusted return. The heart of Taleb’s argument is that standard deviation is only narrowly informative because it was designed for data that’s normally distributed. For example, the distribution of height among adult men in the United States is normally distributed, following a symmetric bell curve. While you may see some NBA players like Shaquille O’Neal towering at 7’ 1”, that’s about as extreme as it gets: you don’t see any 10-foot-tall players dunking on the basketball court, just as you don’t see any adults who are one foot tall. While standard deviation makes sense in this symmetric setting, it falls apart when the distribution is highly skewed, with extreme outcomes on either end. Individual stocks, for example, can lose no more than 100% of their price, but they can gain multiples of their price in a single year, resulting in a right-skewed distribution with a thick tail of highly positive outcomes. There is nothing particularly “standard” about deviations within this asymmetric distribution. That is why Taleb is critical of financial metrics that rely on standard deviation.
In his newest book, Statistical Consequences of Fat Tails, Taleb argues “Beta, Sharpe ratio and other hackneyed financial metrics are uninformative … [because] practically every single economic variable and financial security is thick tailed.”
As we showed last week, it is theoretically possible to have financial securities that score very well on the Sharpe ratio’s “risk-adjusted” basis (which you cannot eat) but quite poorly on the real-world objective of maximizing returns (which you can eat).
But does this theory match reality? Does Taleb’s claim about thick tails show up in your stock portfolio? This week, we’ll look at actual historical returns from growth and value stocks to show where you would have gone hungry and where you would have starved by following the Sharpe ratio.
Below, we present long-term returns for value and growth stocks in the United States. The results look similar to what we saw last week when comparing Asset A and Asset B. As shown below, value stocks have compounded at 12.6% per year, outpacing growth stocks which compounded at 9.6% per year. But since the value returns had more frequent volatility than growth in both directions, the value strategy has a lower Sharpe ratio.
Figure 1: Comparison of Value and Growth in the US (1926–2020)
Source: Ken French data library and Verdad research. All available returns are shown from July 1926 to June 2020. Valuations are measured in terms of Price/Book. Value stocks are defined here as the cheapest 20% of firms in the market and growth stocks are defined as the most expensive 20% of firms in the market.
The mean error measures the average difference between returns in an individual year and the long-term average that represents an expected return of 12.6% per year for value and 9.6% per year for growth. The mean error is more positive for value, indicating that value tends to deliver bigger positive surprises than growth. This suggests that the distribution of value returns is more right-skewed, with big rallies that investors could miss out on if they underweight value because of its lower Sharpe ratio.
So when did those who underweighted value go hungry, and when did they really starve to death in the history of stock returns? Since the Sharpe ratio is ostensibly about “risk,” we decided to highlight the differences in real downside risk between cheap and expensive stocks. To pinpoint where things went really wrong, we used the historical price-to-cash-flow decile returns (cheapest 10% for value and most expensive 10% for growth). And to make this even more “real” we included growth stocks the way most retail mutual funds and ETFs might package them to investors: weighted by the market cap of each company. Value portfolios are presented with equal weights—the way a capacity-constrained deep value manager would aim to implement.
Below are the historical drawdowns on growth and value stocks over the past 70 years. In the top panel, we show cap-weighted portfolios of profitable but extremely expensive growth stocks versus equal-weighted deep-value portfolios. Below that, we show cap-weighted portfolios of unprofitable growth stocks versus equal-weighted deep-value portfolios. These comparisons represent the most crowded versus the least crowded portfolio construction rules.
Figure 2: 70-Year Impact of Crowded vs. Uncrowded Drawdowns
Source: Ken French data library. Data on cash-flow-to-price goes back to 1951.
Note how “stable” growth was at staying down for decades at a time, thereby producing a pretty good Sharpe ratio. This is dangerously uninformative for risk estimates given actual history. We can see that although value drew down to similar depths as growth, value often snapped back more quickly, as demonstrated by its thinner shaded area along the horizontal time series. This whipsaw of drawdowns followed by sharp recoveries in value registers as a higher standard deviation, as value’s lower Sharpe ratio unhelpfully tells you. But it’s precisely because of these sharp, surprise rallies that value has been able to recover faster from historical drawdowns. It seems volatility may be better thought of as noise, rather than risk.
If we think about risk differently, as the possibility of losing money and not rebounding (value draws down frequently but is highly mean reverting), expensive unprofitable firms win the Hall of Fame Risk Award. As you can see in the bottom panel of Figure 2, unprofitable growth stocks that were purchased in the late 1960s didn’t break even until the early 1980s. Profitable growth stocks were not quite as bad but displayed the same general pattern as you can see in the top panel. These were lost decades in growth stocks (and back-to-back lost decades in unprofitable growth firms).
When does this Long-Term Capital Impairment seem to happen? Are we relegated to throwing our hands up with the nihilism of Taleb after acknowledging that we can’t know the true distribution of security returns from the historical distribution alone? Are the prolonged famines in growth random acts of the heavens that strike without any forewarning or opportunity for repentance?
Fortunately, the shocking “Black Swan” surprises of asset price returns did not show up completely unaccompanied. Turns out, asset prices seemed to matter for asset pricing models. In the time leading up to past lost decades for growth, valuations went up considerably for growth stocks. And with those exuberant growth valuations, the size of the average growth stock compared to the average value stock skyrocketed, as shown in the figure below. The solid line (measured on the left axis) shows how much bigger the average growth stock was relative to the average value stock at each point in time. The shaded area (measured on the right axis) shows the excess return of value stocks relative to growth stocks over the subsequent 10 years. The decades of massive value outperformance (and growth famines) seem to have been presaged by the widest price divergences between growth and value.
Figure 3: Average Market Cap of Growth Decile Divided by Value Decile, and Forward Relative Returns
Source: Ken French data library. Data on cash-flow-to-price goes back to 1951.
In our view, holding extreme growth stocks has historically impaired capital over horizons so long that some investors were not around to see a recovery. We would call that real risk—a risk that we think is swept under the rug in a Sharpe ratio that measures the frequency of transient shocks rather than capturing the risk of long-term capital impairment.
One way to quantify the risk of long-term capital impairment would be to simply divide the long-term compounding rate by the amount of time an investor would have spent materially below water in drawdowns. This “Less-Blunt Ratio” doesn’t suffer from the criticisms that a Sharpe (or Sortino) ratio would because it does not assume normally distributed returns.
Returning to our original example in Figure 1 with the price-to-book performance of value and growth stocks since 1926, the Less-Blunt Ratio would look like this over the last century of market gyrations.
Figure 4: Comparison of Value and Growth in the US (1926–2020)
Source: Ken French. Price-to-book data goes back to 1926.
Growth stocks spent ~50% more time in significant drawdowns compared to value stocks over the last century. As we saw earlier, the main reason for this is because the distribution of growth returns appears to be less skewed towards positive surprises (i.e., a lower mean error). Therefore, growth stocks have historically been slower to recover from drawdowns.
The Sharpe ratio for these same portfolios in Figure 1 seemed to prefer growth stocks, but the “Less-Blunt Ratio” here in Figure 4 suggests you got about twice as much compounded wealth per amount of time you were temporarily drawn down by value stocks. We believe this is a more meaningful and less misleading representation of the risk-reward relationship for most investors.