In 1996, Sharpe ratio was created by William Sharpe. Ever since then it’s been used as the referenced risk in finance. It is that popular because of its ease of use. In 1990, Professor Sharpe was awarded a Nobel prize in Economic Science for his effort towards CAPM. And this later contribute to its credibility.
What is sharpe ratio
The Sharpe ratio is number that adjusts a portfolio’s past performance—or expected future performance—for the excess risk that was taken by the investor.
The ratio formula is given here as:
S(x) = (Rx – Rf)/ StdDev(X)
X= the investment, Rx = x average return rate
Rf = best available rate of return, StdDev(X) = standard deviation
A. Rx i.e. return, if normally shared, may be per year, month week or per day. This then reveal the shortcoming of the ratio; all returns on asset are not often normally shared.
Kurtosis: This is the peakedness or flatness of graph of a frequency distribution
skewness: This is a headache to the ratio because standard deviation may not be an option when these problems occur. Sometimes, it can be risky to apply this formula when returns are not in normal distribution.
B. Risk-free rate of return (rf): This is applied to reveal if one is appropriately rewarded for taking further risk. Normally, the most archaic in U.S T-bill is risk-free rate on return. Though this kind of security is more stable, despite risk-free security has been debated by some that it supposed to match the period of comparable investment.
For instance, equities still remain asset that persist for long period. Perhaps we should not compare them with the long period risk-free asset present: IPS was issued by government? Applying IPS that can persist for long time would result into different ratio value, because normally under interest rate clime, T-bills have lesser returns compare to IPS.
For example, a decade index returned of three percent of year 2017 on inflation-protected securities was reported by BARCLAYS US TREASURY.
In contrast, within same duration of time, 7.4% index returned was reported by S and P 500. One may debate that investors giving preference to equities over bonds were fairly rewarded. If Sharpe ratio have bond index of 1.16% against 0.38% equity index means equities asset are riskier.
Since we’ve gotten excess return through subtracting risk-free rate of return from the return of the risky asset, hence there’s need to divide the answer by standard deviation of calculated risky asset. As stated above, as the number rises, the investment gets better.
The way of sharing the returns is Sharpe’s ratio soft rot. Bell curves were employed for convenience mathematically according to Nassim Nicholas and Mandelbrot in 2005.
Bell curves also never take big shift into account.
Nevertheless, leverage do affect ratio if standard deviation is small.
The return as well as the standard deviation can be two times their original size without hitches.
There’s an issue if the denominator is becoming too high. For instance, a stock price that’s supported 10 to 1 without much ado may drop by 10%, this is corresponding to 100% fall in startup capital.
The sharpe ratio and the risk
Knowing the relationship that exist between risk and Sharpe ratio is from calculating the denominator also refers to as total risk. Variance is calculated by squaring the standard deviation i.e. the denominator.
Why did Sharpe pick denominator to balance excesses? Since we are aware that Markowitz comprehend variance- which is one the way of measuring dispersion in statistics, something the investor detest. Standard deviation’s unit is the same as the measured data series.
Here are the examples showing reasons why investors should be mindful of variance:
Any investors are at liberty to pick 3 portfolios, having the expectation of returns of 10% on all in ten years.
The table given below depicts the given expectation. Investment horizon returns gained is shown per annum.
From the table it’s shown that standard deviation shifts return from expectation.
In the absence of risk standard deviation is zero. This means expectation is equal to returns.
Expected Average Returns
Year Portfolio A Portfolio B Portfolio C
Year 1 10.00% 9.00% 2.00%
Year 2 10.00% 15.00% -2.00%
Year 3 10.00% 23.00% 18.00%
Year 4 10.00% 10.00% 12.00%
Year 5 10.00% 11.00% 15.00%
Year 6 10.00% 8.00% 2.00%
Year 7 10.00% 7.00% 7.00%
Year 8 10.00% 6.00% 21.00%
Year 9 10.00% 6.00% 8.00%
Year 10 10.00% 5.00% 17.00%
Average Returns 10.00% 10.00% 10.00%
Annualized Returns 10.00% 9.88% 9.75%
Standard Deviation 0.00% 5.44% 7.80%
How to use sharpe ratio ?
Sharpe ratio maybe used to measure return, can also adjust risk so as to compare investment manager’s performance.
For instance, say one investment manager makes fifteen percent returns and the other twelve percent return. The latter looks excellent in performance. Though the latter took higher risks than the former, but the former risk-adjusted return may be better. To buttress this example, 5% free-risk rate is available, the first managers has eight percent standard deviation, five percent for the second manager. The first would realize Sharpe ratio of 1.25. then 1.4 goes to the second manager, this is better compare to the first manager. Hence as a result of this calculation, the second manager depending on the risk-adjusted got better return.
Ratio 1: Good
Ratio2: Very good
Evaluation of risk and compensation is done together while making investment decisions, and this is the main focus of Modern Portfolio Theory.
Generally, variance or its square root drifts compensation away from the investor. So in order to choose investment it is advisable to deal with risk and reward together. Sharpe ratio will be helpful in making investment decision that will yield bigger returns even when the risk is considered.