“A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, ‘This is where the light is.’” – David H. Freedman
The way people measure portfolio performance, and the performance of things like hedge funds and mutual funds, is the product of one economist’s bright idea.
In 1966, William F. Sharpe laid the cornerstone of contemporary fund analysis with his introduction of the eponymous Sharpe ratio. Simply put, the Sharpe ratio provides a quantifiable, one-dimensional measure for the performance of the risky part of a portfolio, i.e., the whole portfolio except for the part of it that is invested in the risk-free asset. In theory, the Sharpe ratio should provide a measure of a fund’s risk-adjusted return.
In the decades since its introduction, this relatively simple ratio has risen to be investors’ go-to measure of fund performance. Pension fund managers and other allocators usually cite mutual funds’ and hedge funds’ Sharpe ratios prominently in their rationales for allocation.
Yet, while it has been a standard tool for many years, the Sharpe ratio is a blunt instrument that deserves far less faith than it enjoys. There are two chief flaws: First, it is an inherently flawed measure that can produce inaccurate measures of risk-adjusted performance. Second, it can be effectively gamed by fund managers.
This article will address each of these problems in turn. But first, let’s take a moment to get a clear understanding of how exactly Sharpe ratios are calculated and used.
The Sharpe ratio for dummies
A portfolio's Sharpe ratio can be calculated in three relatively simple steps.
First, we take a fund’s historical monthly return data (netting out fees, of course) and compute an average. Next, we subtract the risk-free rate from this average (we can take a U.S. Treasury bond’s interest rate as a suitable substitute for the theoretical risk-free rate, as is common practice in securities analysis). Finally, we take this number and divide it by the standard deviation (the variance from the mean return). The result is the Sharpe ratio. Simple!
To have statistical power, this calculation must be performed for the entire risky part of the portfolio combined, not on a discrete part of the portfolio, such as individual assets or group of assets.
Pension fund managers and other asset allocators love the Sharpe ratio because of its simplicity and comparability across various portfolios. For years, these big pools of capital have been venturing deeper into the universe of mutual funds and hedge funds in pursuit of returns that can meet the ballooning obligations owed to retirees under defined benefit plans. Sharpe ratios are at the forefront of allocation decisions involving hundreds of billions of dollars and affecting millions of individuals.
Yet, while taking the risky part of a fund’s portfolio as a whole and calculating its Sharpe ratio allows, in theory, for a measurement of that portfolio’s risk-adjusted returns, theory does not always play too well in practice. The problems really start to show when theory collides with reality.
Too blunt a tool
The Sharpe ratio is arguably the widest known and most widely used measure of performance in the asset management industry, but it is frequently misused even by investment professionals.
Sharpe never envisioned his ratio being used to discriminate between different investment products, yet in practice that is exactly how it is often used. The Sharpe ratio was conceived as a basic measure of the optimal construction of the overall “risky portfolio,” but that is not how it is employed. The result is some highly questionable comparative analysis between fund offerings.
Even when used as intended, the Sharpe ratio is a deeply flawed measure – flaws that are compounded by its pervasive use across the asset management industry. The problem here is the world is a dynamic system, not static. The ratio depends on stable statistical distributions to function. Alas, the world is not too fond of stability.
Perhaps if the statistical distribution of returns was well behaved, then the Sharpe ratio might actually serve as a reasonable indicator of a given investment fund’s risk-adjusted performance. Unfortunately, extreme, low-probability events are an eternal part of financial markets (just look at the financial crisis of 2008 for a recent example of that). The truth is there are a wide range of asset classes and trading strategies that are highly susceptible to such low-probability events, and more still do not have well-behaved distributions of returns even in stable market conditions.
Let’s take a real-world example of the painful consequences of believing too strongly in the power of the Sharpe ratio: In 2000, the Art Institute of Chicago invested virtually its entire endowment in a hedge fund that had posted the best Sharpe ratio in the industry for several years in a row. The fund’s strategy was actually very simple, built around writing put options. That strategy works just fine in a sustained bull market. Unfortunately, a relatively minor dip in the stock market in 2001 was enough to obliterate the fund and more than $30 million of the Art Institute’s endowment. In the end, there was not even legal recourse for the Art Institute or other investors that lost their money in the same fund. After all, there was no chicanery since the fund’s strategy was widely known. The problem was the investors were looking at the wrong measurement and assigning it far too much weight.
Yet, despite cases like that of the Art Institute, Sharpe ratios remain a staple (if not the staple) of fund allocation decision-making. For investors thinking about handing money over to a fund manager, think twice about how you judge performance.
Gaming the system
The Sharpe ratio is also susceptible to manipulation, a risk common to all simple quantitative methodologies. Fund managers are paid to perform, which is why they are conventionally paid performance fees that are calculated as a percentage of their fund’s total returns. If investors in funds perceive the performance and quality of a fund is governed by the Sharpe ratio, then it may prove to be in the interest of fund managers to make investment decisions that enhance that measure even if it is not in the interest of the investor.
The subprime mortgage crisis of 2008 presents an evocative example of the damage “gaming” the Sharpe ratio can produce: Imagine a financial intermediary takes a bundle of subprime mortgages into a security that produces, say, an 8% coupon annually. We then check the U.S. Treasury yield to find it pays 3% annually. A hedge fund manager could borrow $100 million in Treasuries, post cash collateral of $5 million and then invest the remainder in the aforementioned subprime mortgage security. So long as things go well, the fund will earn $5 million per year from a $5 million cash investment, i.e., a 100% return annually. It is a rather trivial trade, but produces astonishing performance. The Sharpe ratio for such a strategy, in good times, is enviable.
Unfortunately, there is a reason subprime mortgages carry a higher yield – a reason financial institutions learned all too well during the financial crisis. Continuing our example, let us assume one day the people who hold the mortgages on the underlying security face a cash crunch and cannot pay the 8% interest, but can still make principal payments. It might sound like a minor glitch, yet the consequences are dire – the fund is now losing $3 million annually on a $5 million investment. Worse still, if the underlying home price drops by just 2% – in other words, only 2% of the capital cannot be repaid – then the fund is busted.
The problem with the Sharpe ratio should be obvious: It cannot ward against investment strategies that carry consistent and significant returns under ordinary circumstances, but that cause catastrophic losses in low probability scenarios.
The perverse incentives in play in the run-up to the financial crisis are far from unique. Other high Sharpe ratio strategies are quite commonplace in financial markets. Really, any strategy that delivers an insurance product will show an abnormally high Sharpe ratio. This is obvious when you think about it since an insurance product delivers stable premiums each year – until the big disaster you are writing insurance against materializes. In financial markets, variance swaps and option writing (for covered call options, put options, etc.) are some of the basic “insurance” products funds can create.
Takeaway for investors
A key thing investors should take away from this discussion is the common measures of fund performance may be common for reasons other than their accuracy. Returning to the quote at the start of this article, we can see that when people try to find ways to measure performance, they may fixate on things that can be measured – whether they are truly indicative of performance or not. Like the drunk rooting around under the light, investors look where the data is without necessarily discriminating as to its quality or predictive power.
The Sharpe ratio is not useless – it can be a decent tool for weeding out overly volatile funds. But using it as a judgement tool for fund allocation is woefully inadequate at best, and prone to catastrophic misjudgement at worst.
There can be advantages for investors to allocate some capital to funds in order to take advantage of their specialized knowledge and strategies. But performance has to be looked on with extreme skepticism and picked over forensically. Hoping for magic ratios to do the hard work of due diligence for you is a guarantee of future pain.
