The nature of returns

The pursuit of yield

Investing is all about making your money work as hard as possible for you. When making a decision about what where to invest we often ask, ‘where can I earn the highest return on my investment?’ Although stocks are generally the best performing asset class most people opt to invest towards real estate or just leaving the money in a high interest term deposit in the bank. Part of the reason for this is that stocks are considered to be a more risky investment and that even though they achieve a higher average annual return, they are generally more volatile. Some people are more comfortable sacrificing the extra yield they could gain through owning stocks for the relative safety of a lower yielding investment with more consistent returns.

growth chart

Growth of house price index, S & P 500 index and money invested in a hypothetical hedge fund. Which is the better investment?

Less is sometimes more

To account for both the consistency of the returns and how much they can deviate from the average, it is perhaps more prudent to quantify the quality of an investment by the risk adjusted return rather than just the average long term return. Determining the risk adjusted return can actually become a difficult task since the overall long-term distribution of returns of an investment can be quite unique. Some investments follow a normal distribution and only have a single mode, whereas others may be multimodal or have other abnormal features which need to be accounted for. Despite this, there are some fairly basic mathematical quantities which can give a good idea of what the risk adjusted return is. Sometimes this can lead to an investment strategy being superior on a risk adjusted basis compared to another despite having lower absolute returns.

Measuring risk adjusted returns

The most popular method for accessing the risk adjusted return is the Sharpe ratio. The Sharpe ratio is a ratio defined as follows:


The risk-free return is usually interpreted as the as short term US Treasuries since this type of investment is considered to be about as safe as it gets – the US has never defaulted on debt, ever.

Beyond the Sharpe ratio

The problem with the Sharpe ratio is that because it looks at the standard deviation of the returns it only really provides a fair comparison if the returns follow a normal distribution. Another drawback is that it penalizes abnormal positive returns just as much abnormal negative returns.

Another measure which can be viewed of as an improvement beyond the Sharpe ratio is the Sortino ratio. The Sortino ratio is defined as follows:


The ratio is the exact same except that now only the negative deviations from a specific target return rate are penalised through the denominator term. This seems to make more sense, since we aren’t really concerned about returns which exceed our expectations – although it may signify inconsistency, these are pleasant surprises!

It’s worth looking into the denominator term since its calculation is a little different to plain, old standard deviation. This is the formula for calculating the standard deviation of the returns for the Sharpe ratio.


For the Sortino Ratio we first must define a Minimum Acceptable Return (MAR). This in itself is a variable and could be simply 0%, the rate of inflation, the risk-free return or some higher yield target. The Target downside deviation is defined as:


It looks similar to the standard deviation formula but only factors in deviations less that the MAR not the mean return and sets deviations above it to 0% when calculating so that they aren’t penalised.

Yet again, just as for the Sharpe ratio, the Sortino ratio tends to be a good measure if the returns follow a normal distribution. Quantifying the risk adjusted return becomes a more complex task when considering non-normally distrusted returns but simple ratios such as these do a reasonable job in practice for most circumstances.

Comparing investments

In order to test out the concept of risk adjusted returns, I’ve chosen to use the S & P 500, the average US house price index (Case- Shiller) and the returns of hypothetical hedge fund, hedge fund ‘X’. For each of them I have compared them over the last 20 years and tabulated the results for the annual average return, just making up numbers for the Hedge fund for the sake of the example. I have assumed a risk free of 1%.The returns for each are tabulated below.

Year S & P / Case-Shiller S & P 500 Hedge Fund
1998 6.45 28.58 1.70
1999 7.69 21.04 3.10
2000 9.25 -9.10 1.30
2001 6.77 -11.89 4.40
2002 9.46 -22.10 5.00
2003 9.82 28.68 3.10
2004 13.64 10.88 1.60
2005 13.51 4.91 0.20
2006 2.22 15.79 4.90
2007 -5.30 5.49 2.00
2008 -11.89 -37.00 3.20
2009 -3.70 26.46 3.00
2010 -3.97 15.06 0.10
2011 -3.80 2.11 1.30
2012 6.47 16.00 3.70
2013 10.65 32.39 0.80
2014 4.40 13.69 1.40
2015 5.09 1.38 4.00
2016 5.25 11.96 5.00
2017 6.20 21.83 1.30
Average – RFR 3.41 7.81 1.56
St Dev 6.81 17.89 1.59
Sharpe 0.50 0.44 0.98
Sortino 0.73 0.68 1.14

As can be seen, despite the S & P having a much higher average return than the other two investments it has the lowest Sharpe ratio since it’s the most volatile. The Hedge Fund on the other hand has the lowest return, with a measly average return of 2.56 %. Yet, on a risk adjusted basis is superior to both real estate and the stock market.

I’ve also calculated the Sortino ratios for the investments, considering a MAR of 3%. This doesn’t really do much to change the order, however if I were to change the MAR to 5%, the order of investments on a risk adjusted basis actually becomes reversed with shares being the best performer and the overall values of the ratio becoming much more of muchness for the three investments – 0.61 for real estate, 0.64 for stocks and 0.54 for the hedge fund.

Risk appetite

What’s important to remember is that everyone has a different appetite for risk and that even though one investment may provide a far better risk adjusted return than another, some may choose the riskier investment because they’re unsatisfied with the absolute return. Most hedge funds consistently underperform the market indices and some may ask ‘why anyone would bother investing their money in them?’ The answer lies in their ability to generate smaller but far more consistent returns, just like the hypothetical one described above. While real estate and shares had big loses in 2008, the hypothetical Hedge Fund still managed to make a profit. Now, the question is, would you choose investing in the Hedge Fund over the S and P 500 index fund or purchasing an investment property?

Personally I wouldn’t; an average return of 2.56 % doesn’t exactly excite me. I would rather something more volatile that on average rises more. This is probably also driven by the stage of my life – if the market crashes and there is a recession, I have enough time before I retire to (probably) realize the long term gain of the riskier investments. Those that are nearing retirement should play it safer and instead sacrifice yield gain for lower volatility. Other things in life can shape our appetite for risk also – having children will like reduce appetite for risk; knowing that there are extra mouths to feed means a more consistent return is required when choosing to invest. The Sharpe and Sortino ratio don’t really capture this appetite for risk although the Sortino ratio can in a way be used for this purpose through adjusting the MAR. Those with greater appetite for risk should choose a higher MAR when assessing investments. This will lead to the risk adjusted returns making far more sense to that individual.

risk appetite

The take home message

When considering what you do with your money, you should always assess not only what level of return is expected but also how rough the ride is going to be along the way. The Sharpe ratio and in my opinion, the superior Sortino ratio are at least something to consider when looking into investments and scrutinizing them beyond the simple average return. Volatility is an important factor to consider, but ones tolerance to it is very much an individual factor which is often based on life circumstances.

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