You will be able to calculate Sharpe and Sortino ratios and judge when a high ratio hides a risk.
A relationship manager shows Marcus a structured income fund with a Sharpe ratio above 2. His own portfolio's ratio, when he works it out, is under 0.4. On that comparison the fund looks five times better. Before he believes it, he needs to know what the ratio measures and which kinds of strategy produce a big one without being any safer.
The Sharpe ratio, named after the economist William Sharpe, divides the return you earned above a risk-free rate by the volatility you took to earn it. It answers a simple question: how much extra return did each unit of wobble buy?
The formula is the average return minus the risk-free rate, divided by the standard deviation of returns. Use the same period for all three, and annualise them together.
The risk-free rate should be one you could actually have earned in Singapore dollars with no real risk, and a Singapore T-bill yield is the natural choice. MAS publishes T-bill auction results and yields on its website. Look up the figure for your period rather than using one quoted here. For the worked example, we'll assume a made-up risk-free rate of 3% a year.
Marcus's ten made-up yearly returns, which include the five years from his returns tab, are 10%, minus 7%, 19%, 6%, 12%, 14%, minus 18%, 16%, 9% and 11%. Their arithmetic average is 7.2% and their standard deviation is about 11.3%. His Sharpe ratio is 7.2 minus 3, divided by 11.3: about 0.37.
A made-up world equity index over the same ten years averaged 9.0% with a standard deviation of about 12.5%, which gives it a Sharpe ratio of about 0.48, so the index paid more return per unit of volatility than Marcus's portfolio did.
Analysts use the arithmetic average in the Sharpe ratio because it fits the statistics underneath. For judging what you ended up with, the geometric figure from module 1 is still the one to quote.
Lesson 2.1 showed that volatility counts a big gain as risk. The Sortino ratio fixes that by replacing volatility with downside deviation, which only counts returns below a chosen target.
To calculate downside deviation, pick the target, here the 3% risk-free rate. For each year, take the return minus the target if it's negative, or zero if it isn't. Square those numbers, average them over all the years, and take the square root.
For Marcus, only two years fall short of 3%, the minus 7% year and the minus 18% year, giving shortfalls of 10 and 21 points. Averaged over ten years and square-rooted, downside deviation is about 7.4%. His Sortino ratio is 4.2 divided by 7.4: about 0.57. The world index scores about 0.84.
Different sources use different targets, zero or the risk-free rate, and some average only over the losing years. Each choice changes the number, so write yours down and use it for everything you compare.
Now back to the relationship manager's fund. Some strategies sell what amounts to insurance. They collect a small, steady premium most of the time and pay out heavily in a rare bad event, and selling put options, writing default protection and some structured products all have that shape. Their return history looks smooth, so volatility is low and the Sharpe ratio is high, right up to the event.
Here is a made-up strategy. For nine years it returns 9%, 6%, 8%, 5%, 7%, 9%, 6%, 8% and 7%. Its average is about 7.2% with a standard deviation of about 1.4%, and its Sharpe ratio is about 3.0. In year ten it loses 30%. Its ten-year Sharpe ratio drops to about 0.04, and its compound return over the decade is about 2.7% a year, below the made-up risk-free rate.
The danger is that nine good years are all you see. A fund launched in a calm period, or a backtest that leaves out a crash, can show a Sharpe ratio above 2 for its whole published life. The ratio can't warn you about a risk the history doesn't contain.
Three other traps are worth knowing. Assets that are priced rarely, such as private funds or property valued once a year, look smoother than they are, which flatters their ratio. A ratio from three years of data is mostly noise. Borrowing to invest leaves the Sharpe ratio roughly where it was, so a fund that doubles both its excess return and its volatility with borrowed money keeps the same score while its drawdowns double.
So when a product shows a high Sharpe ratio, ask three things: how long the history is, whether it includes a crisis, and what the strategy loses when things go wrong. If the answer to the last is "we've never had a losing year", that's the moment to ask harder questions.
For the activity, take your portfolio's yearly or monthly returns, which you already have from lesson 1.8, and one benchmark's. Look up the T-bill yield for your period on the MAS website, and calculate both ratios for each.
Calculate Sharpe and Sortino ratios for your portfolio and one benchmark, using a T-bill yield you looked up on the MAS website.
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