Risk-adjusted return: Sharpe Ratio

My portfolio started in January 2013 returned 52.4% against the KLCI of 14.0% for the past one year. The excess return is thus 38.4%. Does that tell us all about the performance of the portfolio?

Return alone-and especially return over short period of time of just one year says very little about the quality of investment decisions. Return has to be evaluated relative to risk taken to achieve it.

Sharpe ratio is a measure that helps investors figure out how much return they're getting in exchange for the level of risk they're taking on. The ratio is written as followed:

Sharpe Ratio, SR=(R_s-R_f)/σ

R_s is the return of the stock

R_f is the risk free rate

σ is the annual standard deviation of the return of the stock.

Created by Nobel laureate William Sharpe, the ratio is intended to be a measure of what an investment returned for each "unit" of risk it carried. The top half of the ratio looks at what a stock or portfolio returned over a set period and subtracts what an investor could have earned in a risk-free investment, over that same period. The denominator is the stock's standard deviation, which measures how much a stock strays from its average performance—in other words, its volatility. The higher the ratio, the more an investor is compensated for the risk he takes on. The Sharpe ratio obtained for the stock is then compared with the Sharper ratio of the broad market, in this case, the KLCI index during the same period.

For the explanation of Sharpe ratio, please refer to the following link:

http://www.investopedia.com/articles/07/sharpe_ratio.asp

The KLCI returned 14% for 2013 with a relatively low standard deviation of return of 8.8% last year. Taking the risk-free rate as 3.5% which approximates the one-year MGS rate, the Sharpe ratio is 1.2.  Hence any stock with a Sharpe ratio greater than 1.2 has a higher risk-adjusted return than the market. So which are the stocks in the portfolio has a higher risk-adjusted return than the market?

Table 1 below shows the computation of the standard deviation (from the share price data from Yahoo Finance) and the Sharpe ratios for the stocks in the portfolio.

Table 1: Risk-adjusted return

It can be seen that although eight stocks in the portfolio made return of more than the return of KLCI of 14%, only five of them have a better risk-adjusted return than KLCI; they are Jobstreet, Prestariang, Pintaras Jaya, NTPM and Plenitude, in that order of excess return. ECS ICT, Kimlun, and Pantech, though have higher absolute returns than KLCI, have lower risk-adjusted return than KLCI.

How about the risk-adjusted return of the portfolio? For those who are interested in calculation of the standard deviation of a portfolio of stocks and its return, please refer to the following link:

http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/advanced-probability.asp

Assuming the stocks are all equally weighted, the portfolio return is the average return of each stocks, which is 52.4% as above. The equally weighted portfolio has standard deviation of 32%. The Sharpe ratio of the portfolio is hence equals to (52.4%-3.5%)/32%, or 1.54. This ratio is bigger than the Sharpe ratio of KLCI of 1.2. Hence it may imply that the portfolio has a higher risk-adjusted return than KLCI.

The Sharpe ratio has its short coming; specifically the measurement of risk using the volatility of the return of its stock prices. However it is about the best idiosyncratic risk-adjusted return quantitative measure we have.

Figure: Sharpe ratio