To some casual critics, the idea of investment returns appears somehow unfair: investors, it may seem, are being paid for already having money. More sophisticated observers realize that, in fact, what investors are compensated for is *taking risk* — that is, for allowing their funds to be used, directly or indirectly, in risky economic projects that may or may not return their money. Understandably, most investors expect higher investment returns when they accept higher risks. But how do investors know if they are well compensated for the risks they take? That is the topic of this blog post, in which we explore the concept of risk-adjusted returns — in particular, the notion of the Sharpe ratio.

##### Weighing risks and rewards

The returns on an investment are generally straightforward to quantify. At its most basic, an investment is just an exchange of some money today for some (hopefully larger) amount of money in the future. The return on the investment is simply how much the original investment amount grew as a result of those future payments, over a given time period.

Risk, however, is a more elusive concept. It can be understood in myriad ways, and may vary by investor, but a widely used indicator of risk is the *standard deviation of returns*, often referred to as the volatility of an investment. The underlying intuition is that if investment returns are more variable, they are less predictable, and therefore riskier to investors.

We illustrate these concepts with some real-life examples. The chart below plots the 2017 monthly annualized returns against standard deviations of a few select asset classes, or major categories of investments.^{1}

This gives us a general sense of what investments yielded what returns, and how risky they were. We can quickly tell that the Dubai stock market did not give investors very attractive compensation for associated risks in 2017. But some other asset classes are trickier to parse: how did US stocks compare to high-yield bonds or liwwa loans on a risk-adjusted basis, given that stocks had both higher returns and higher risks?

In order to get a more direct comparison of what asset classes yielded "good" returns given their volatility, we turn to another analytical tool: the Sharpe ratio.

##### Comparing Sharpe ratios

The Sharpe ratio is a measure of the risk-adjusted return of a portfolio of assets, first introduced by Nobel Prize-winning economist William F. Sharpe. The Sharpe ratio tries to answers the question: for each unit of risk you take, what returns are you getting in exchange?

It does so by dividing the "excess return" of an asset or portfolio with the standard deviation of its returns. "Excess return" refers to the additional returns generated by the asset above and beyond some theoretical "risk-free rate," or RFR. For practical purposes, calling this rate "risk-free" is a bit of a misnomer, since no investment is truly without risk. In reality, we can think of it as the least risky baseline rate available to investors. Conventionally the rate on the three-month U.S. Treasury bill is used as the RFR, and since we are dealing here with assets all denominated in U.S. dollar-pegged currencies, it is appropriate for our purposes.

Calculating the Sharpe ratio is now simple; it's just

```
Sharpe Ratio = (Average Return - RFR) / (Standard deviation of returns)
```

This gives us a more direct way of comparing how well different investments compensate us for the associated risks. The chart below presents the Sharpe ratios of the asset classes from the scatterplot above.

This makes it clear that taking risk into account, liwwa loans provide good compensation for risk, relative to other asset classes.

##### Explaining high Sharpe ratios Jordanian SME debt

A Sharpe ratio above 2 for monthly returns is unusually high. As a point of reference, U.S. real estate investments during the boom years of the early 2000s had a Sharpe ratio around 1.35.^{2}

How can we observe such a high Sharpe ratio for Jordanian small business loans? The efficient markets hypothesis suggests this should not persist, since investors will pile into such an asset and bid up its price, thus bringing its risk-adjusted returns in line with other asset classes. However, this depends on the assumption that the asset is traded in an efficient market: one characterized by perfect information, low transaction costs, and low barriers to entry. This may be true of large markets in the West, like the New York Stock Exchange or the market for UK gilts, but it is far from true for small business debt markets in Jordan. The practical difficulties of entering this market for most investors, along with the higher cost of acquiring information and executing transactions, mean that abnormally high risk-adjusted returns can persist in a way that they can't in large, publicly traded markets.

liwwa.com provides a rare opportunity for investors to tap into such a market, by solving the market entry, information and transaction problems for investors through a simple online interface.

##### A final word on portfolio diversification

Finally, the point of the Sharpe ratio is not necessarily to decide if one asset class is "better" than another. A more reasonable usage of the Sharpe ratio is to help investors decide whether and how much of an asset to include in their overall portfolio, based on how the new asset would affect the portfolio's risk/return profile. This question of *optimal portfolio allocation* will be the topic of an upcoming blog post.

For US stocks, we use the S&P 500 index. For Dubai stocks, we use the DFM General Index. For US high-yield bonds, we use the S&P High Yield Corporate Bond Index. For Commodities, we use the GSCI. Data on liwwa loans comes from liwwa Inc, and includes all loans maturing in 2017, reported net of fees, late payments, defaults. For liwwa loans, we assume a fully diversified portfolio that participated in all loans offered through www.liwwa.com. ↩

Frank J. Ambrosio, "An Evaluation of Risk Metrics,"

*Vanguard Investment Counseling & Research*, https://personal.vanguard.com/pdf/flgerm.pdf, p.6 ↩