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Give your portfolio a Sortino sanity check

The Sortino ratio is a simple but effect way investors can calculate the inherent risk in their portfolios. James Norrington explains how it works
September 26, 2014

Back in 2012, to help readers choose an appropriate asset allocation strategy for their personal objectives and risk tolerance, Investors Chronicle suggested three models for 'cautious', 'balanced' and 'adventurous' investors ('The Ideal Portfolio', 11 May 2012). These looked at the approximate mix of shares, bonds, property, cash and other assets (eg, gold, stamps, fine wine, etc.) that each type of investor should aim to own. Revisiting the models, in the coming months I aim to create my own portfolios for each. As part of the process, I want to consider charges and also try to start with different hypothetical amounts to reflect alternative circumstances. After all, how a novice investor using their £15,000 Nisa allowance diversifies risk will be different to the average Investors Chronicle reader, who has a portfolio worth £789,402, according to our last commissioned research.

In running the Ideal Portfolios the obvious aim will be to maximise returns but also to do so relative to the 'riskiness' of the investments made. This in part involves using elements of portfolio theory to ensure that the required rate of return is achieved with the least volatile mix of investments. First and foremost, the task is to make the portfolios as robust as possible to cope with any unforeseen and unpredictable downside. In other words we are managing two strands of risk, one theoretical and in part quantifiable and the other 'real-world' risk of leaving oneself vulnerable to an unexpected shock that could wipe out large swathes of capital.

As readers of our article 'Predicting the Unpredictable' (8 August 2014) will recall, the valid critique of many risk-modelling techniques based on the mathematical normal distribution of returns, is that they do not reflect the magnitude nor the 'fat-tail' impact on returns over time of big market shocks. By far the most reliable way to ensure a portfolio's robustness in the face of another 'Black Swan' event such as 9/11 or the collapse of Lehman Bros is broad asset class diversification.

With this in mind, investors might ask whether it is worth ever deviating from the cautious Ideal Portfolio model. The answer is, it depends on your time horizons. The real world risk of what you might lose has two parts to it; what you might lose by your actions and alternatively what you might lose or miss out on by your inaction (or acting timidly). An obvious example of the risk of investing too conservatively is in saving for the long-term goal of retirement but overly allocating capital to assets with returns that fail to adequately outpace inflation. This can result in a lower standard of living in retirement - a very real and dangerous risk. Despite their limitations in allowing for big market shocks, the risk management models in existence can make a useful contribution to strategic asset allocation decisions and reviews.

 

 

Modelling for optimal risk-return

In financial theory the proxy for risk is asset price volatility, which measures the upward and downward deviation of returns from the mean. This definition of risk includes the upside that investors want as well as the downside they don't.

However, tracking volatility relative to the benchmark is important to understand the market-correlated risk/performance or 'beta' (β) of investments. In the capital asset pricing model (CAPM), which is an extension of Markowitz's portfolio theory, beta represents the market risk that cannot be diversified away within an asset class and is part of the calculation to work out the premium an investor should expect from an individual security or portfolio. Our feature 'The Maths Behind Investing' (13 September 2013) provides a full explanation and critique of portfolio theory and CAPM and how to use it to help value securities.

CAPM undoubtedly has its place in assessing the worth of individual investments, but for the purpose of managing the Ideal Portfolios I also want to look to some other more recent models and principally those that isolate downside in measuring performance against risk.

One of the main contributors to the evolution of CAPM was William Sharpe and his name is given to the ratio that measures excess returns (ie, that those over the 'risk-free' rate, often taken as the yield on government bonds) per unit of deviation/risk. The Sharpe Ratio has been widely adopted as a performance indicator in the asset management industry but the obvious criticism is that, as it is calculated by dividing excess returns by volatility, it penalises not only downside but also outlying positive returns.

No investor loses sleep over upside and an alternative metric is provided by the Sortino Ratio. Sometimes incorrectly calculated as excess returns divided by standard deviation of negative returns, the true Sortino ratio was actually devised to consider below target returns. As pointed out in a recent paper by Red Rock Capital, titled 'Sortino: a sharper ratio', when calculated right the Sortino ratio takes into account the frequency and the magnitude of below target returns. The higher the Sortino ratio, the better the excess returns relative to below target performance, so when we have a specific return in mind it is a useful tool to compare strategies. We explain how to calculate this ratio [above/below, etc].

Testing risk-adjusted portfolios

In 2012 we compared a simplified version of an adventurous allocation model, made up of shares, gilts, gold and cash (70:20:5:5), with investing in just shares. I have re-run this model for the 10 years from September 2004 and the 15 years since 1999, as well as versions for balanced (50:40:5:5) and cautious (20:60:5:15) strategies. The version two years ago took total returns of the FTSE 100 as the benchmark for shares but I prefer to use the FTSE 350.

As a first step, we need a target rate of return. In September 1999 the Bank of England base rate was 5 per cent and the yield on gilts (issued 15/08/99) was 4.8 per cent. The respective figures for 2004 were 4.75 per cent and 4.81 per cent so I've assumed that in both cases rational investors would pursue a target annual rate of return of at least 6 per cent to compensate them for taking higher risk.

Looking at the 10-year figures, we can see that the balanced portfolio has the highest Sortino Ratio of 0.822. This reflects the fact that it has averaged annual returns of over 7.87 per cent, has only twice delivered returns below the target level and that the magnitude of these disappointments has been limited; neither of the below target performances were negative. Investing in just shares or according to the more adventurous allocation model would have achieved a higher return over the same period but the lower Sortino Ratios reflect the greater frequency and significance of below target returns, in particular during the financial crisis.

Over the longer 15-year period, the slightly negative Sortino Ratios are demonstrative of what has been a very testing period for investors since 1999. Two savage bear markets in equities in 2000-03 and 2007-09 have been followed by a period of low interest rates and suppressed bond yields, making it hard for any investor to consistently achieve a 6 per cent target annual rate of return set back in 1999.

However, the true headline figures are of course those of compounded total returns. In spite of considerable headwinds, just investing in the FTSE 350 and reinvesting dividends would have made 45.08 per cent adjusted for retail price index (RPI) inflation. The figure for the asset allocation strategies would not only have reduced the pain of the bad times for equities by mitigating the stock market's falls; the inflation-adjusted returns are 67 per cent for adventurous, 73.56 per cent for balanced and 70.95 per cent for cautious. This illustrates that, in spite of the downside risk and some pretty adverse conditions at times, historically it has paid to stay invested and let the power of compounding work its magic over the long term.

Once more casting our eye over the performance since 2004, buoyed by great years for the FTSE 350 in 2010, 2012 and 2013 in particular, in terms of total returns a higher allocation towards shares would have done best but it is easy to say this in hindsight. Back in 2008 and early 2009, when it felt like financial armageddon, investors would have been delighted with the defensive qualities of our balanced and cautious asset allocation strategies, both of which would have avoided negative returns throughout the crisis. True, the balanced strategy highlighted by its Sortino ratio would have made less money in the bull market in shares but considering the magnitude of the falls in equities in the early 2000s and again throughout 2007-09, it has been shown to experience less painful drawdown following unpredictable events.

Some investors, especially those with a longer time frame for their objectives, may choose to risk a more adventurous strategy during bull markets in equities. As part of our Market Tactics series I'll be looking for tactical asset allocation opportunities to generate more excess returns for our ideal portfolios. Profits are more concrete than risk ratios, so flexing an asset allocation strategy is fine to take advantage of a powerful uptrend in an asset. However, continuing to heed risk metrics as key performance indicators is important to avoid getting carried away, maintain discipline and a focus on overall objectives. In the example models we've looked at here, I've taken benchmarks for the asset classes. In managing our strategies I'll be looking at individual investments and how adding these will adjust the risk profile of our overall portfolios. The hope is that this focus will help the portfolios generate 'alpha' (α) - the positive returns that are not due to market risk.

 

How to calculate the Sortino Ratio

The Sortino Ratio considers excess returns relative to the risk of below target returns.

Part One: To calculate the numerator of the ratio

Looking at the returns of our balanced asset allocation strategy since September 2004, we achieved returns of 16.28 per cent, 11.67 per cent, 6.15 per cent, 0.06 per cent, 1.17 per cent, 12.75 per cent, 6.48 per cent, 9.80 per cent, 7.06 per cent and 6.71 per cent. After subtracting the target 6 per cent return from each of these figures, the average over performance or 'excess return' is 1.87 per cent.

Part Two: To calculate the denominator

All but two of the returns since 2004 beat the target return of 6 per cent. When considering the deviation of below target returns, we must still account for the returns that outperformed. All returns above 6 per cent are considered as below target returns of zero. We work out the average of the squares of all below target returns, including the eight below target returns of zero. The square root of this figure provides us with the target downside deviation, which in this case is 0.022772.

The Sortino Ratio is equal to 1.87 per cent - ie, 0.0187, divided by 0.022772, which is 0.821 or (0.822 thanks to rounding of inputs in excel)

 

 

Other metrics to help manage risk

When looking at investments to add to our ideal portfolios I want to consider how they will affect the overall risk profile of the portfolios and also look at the premiums on offer to investors for past riskiness of the investments. Here is a brief summary of some of the metrics I will look at in more depth as part of that process.

Sharpe Ratio:

The Sharpe Ratio is a measurement of returns relative to asset price volatility.

Adjusted Sharpe Ratio:

The adjusted Sharpe Ratio also looks at asset price volatility but as well as standard deviation it measures the Skewness and Kurtosis (peakedness) of the returns time series. This measure isn't perfect but it makes more of an effort to take account of overreaction and underreaction in markets.

Calmar ratio:

The Calmar Ratio is used to determine returns relative to drawdown risk - ie, the maximum drop in an assets value between two peaks. It is a useful measure as it takes into account the real pain felt by investors during bad periods.

Modified value at risk:

This is an estimate of the minimum expected loss of a security or portfolio over time and at a desired level of significance. Like the adjusted Sharpe Ratio, it takes into account the Kurtosis and Skewness features of the returns distribution.