kcchongnz has left a new comment on your post "Shall we avoid risks? - kcchongnz":

Risk-adjusted return 

My portfolio of 10 stocks posted in i3 in January 2013 returned 52% for the year. Is that good? I will talk about it when KLSE closes for the year 2013. 

In actual fact, return alone-and especially return over short periods of time-says very little about the quality of investment decisions. Return has to be evaluated relative to risk taken to achieve it. How do we evaluate it then? 

First we have to compare the return of a benchmark, and let say we just take KLSE as one. KLSE’s total return including dividend is about 16% for 2013 with a standard deviation, sigma, of 10% say. One may jump into conclusion that a stock in the portfolio, Kimlun with a total return of 26% is better. But let say the sigma of Kimlun is 20%, does Kimlun make a better risk-adjusted return? 

A simplistic way to look at it is Kimlun returns 1.3 (26%/20%) per unit risk compared to 1.6 of the KLSE. Hence Kimlun does not do better than the market in a risk-adjusted basis. 

The other way to look at idiosyncratic risk is the use of a more acceptable ratio, the Sharpe ratio; 

Sharpe Ratio, SR=(Rs-Rf)/Sigma. 

Where Rs is the return of stock, Rf the risk free rate, say 3.5%. 
In this case, Kimlun’s risk-adjusted return of 1.13 is still inferior to the 1.25 of the market. 

In evaluating the performance of a diversified portfolio of stocks, I like the following way: 

Risk-adjusted return y = alpha + Beta * x, 

where alpha is the excess return, Beta is a risk measure, 1.0 for the broad market, and x is the return of the market. In theory, Beta of s stock is the slope of the regression of the return of the portfolio against the return of the market, and Beta of the portfolio is the weighted average of Betas of individual stocks. 

If you have a portfolio of concentrated (of the same industry) and volatile stocks, Beta can be very high, say at 2.5. So if the return of your portfolio is 35%, and the return of the market is 16%, your excess return, alpha, is minus 5% (35%-2.5*16%). You do no better than the market. 

However, if you have a diversified portfolio of stocks with low correlations, and stable and less volatile companies, say with a Beta of 0.8, meaning less volatile than the market, and a return of 13%, your alpha is positive at 0.2% (13%-0.8*16%). You outperform the market even though the return is not as good as the market. 

You may carry out regression to get the Beta value of a portfolio. But I still don’t buy the notion that a portfolio which moves more than the market is a risky portfolio. However in practice, it is more of a judgement. Judgement of Beta is a skill of an experienced investor, not anybody. 

KC Chong (28/12/13)

Posted by kcchongnz at Dec 28, 2013 05:09 PM