BUILDING SHARPE OPTIMIZATION STOCK PORTFOLIOS AND PERFORMANCE ANALYSIS

SCOPE OF PRESENTATION

• INTRODUCTION• SHARPE RATIO & OTHER PERFORMANCE

MEASURES• COMPARING PERFORMANCE MEASURES• METHODOLOGY ADOPTED• CONCLUSION • RECOMMENDATIONS

NEED FOR PERFORMANCE ANALYSIS

• MUTUAL FUNDS THE MOST APPROPRIATE OPPORTUNITY FOR SMALL INVESTORS

• AS FINANCIAL MARKETS BECOME MORE COMPLEX & SOPHISTICATED , INVESTORS NEED A FINANCIAL INTERMEDIARY

• MODELS LIKE SHARPE PROVIDE PROFESSIONAL EXPERTISE ON SUCCESFUL INVESTING

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SHARPE RATIO

• The Sharpe ratio is a reward-to-risk ratio that focuses on total risk.

• It is computed as a portfolio’s risk premium divided by the standard deviation for the portfolio’s return.

p

fp

σ

RRratio Sharpe

SHARPE RATIO FOR A LAYMAN

• IT QUANTIFIES THE RISK EFFICIENCY OF AN INVESTMENT

• EQUAL TO EFFECTIVE RETURN(ACTUAL RETURN MINUS RISK FREE RATE) OF AN INVESTMENT DIVIDED BY STANDARD DEVIATION

• A HIGH SHARPE RATIO SIGNALS AN INVESTMENT WITH GREATER RISK EFFICIENCY AND IS DESIRABLE

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OTHER PERFORMANCE MEASURES

The Treynor Ratio• The Treynor ratio is a reward-to-risk ratio that

looks at systematic risk only.• It is computed as a portfolio’s risk premium

divided by the portfolio’s beta coefficient.

p

fp

β

RRratio Treynor

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OTHER PERFORMANCE MEASURESJensen’s Alpha• Jensen’s alpha is the excess return above or below the security market

line. It can be interpreted as a measure of how much the portfolio “beat the market.”

• It is computed as the raw portfolio return less the expected portfolio return as predicted by the CAPM.

Actual return

CAPM Risk-Adjusted ‘Predicted’ Return“Extra” Return

RREβ R Rα fMpfpp

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Comparing Performance Measures, I.

• Because the performance rankings can be substantially different, which performance measure should we use?

Sharpe ratio:

• Appropriate for the evaluation of an entire portfolio.

• Penalizes a portfolio for being undiversified, because in general, total risk systematic risk only for relatively well-diversified portfolios.

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Comparing Performance Measures, II.

Treynor ratio and Jensen’s alpha:

• Appropriate for the evaluation of securities or portfolios for possible inclusion into an existing portfolio.

• Both are similar, the only difference is that the Treynor ratio standardizes returns, including excess returns, relative to beta.

• Both require a beta estimate (and betas from different sources can differ a lot).

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Sharpe-Optimal Portfolios, I.• Allocating funds to achieve the highest possible Sharpe ratio is said to be

Sharpe-optimal.

• To find the Sharpe-optimal portfolio, first look at the plot of the possible risk-return possibilities, i.e., the investment opportunity set.

ExpectedReturn

Standard deviation

××

××

×

×

××

×

×

×× ×

×

×

×

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ExpectedReturn

Standard deviation

× A

Rf

A

fA

σ

RREslope

Sharpe-Optimal Portfolios, II.• The slope of a straight line drawn from the risk-free rate to where the

portfolio plots gives the Sharpe ratio for that portfolio.

• The portfolio with the steepest slope is the Sharpe-optimal portfolio.

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Sharpe-Optimal Portfolios, III.

METHODOLOGY ADOPTED

• CALCULATION OF ALL THE COMPOSITE PERFORMANCE MEASUREMENT RATIOS

• RANKING THE SELECTED 24 MUTUAL FUNDS AS PER THE RATIOS OBTAINED

• APPLICATION OF SHARPE OPTIMIZATION TECHNIQUE TO KOTAK 30 EQUITY GROWTH MUTUAL FUND

RANKING OF SAMPLE MUTUAL FUNDS ON BASIS OF TREYNOR RATIO

RANKING OF SAMPLE MUTUAL FUNDS ON BASIS OF TREYNOR RATIO

RANKING OF SAMPLE MUTUAL FUNDS ON BASIS OF JENSON RATIO

RANKING OF SAMPLE MUTUAL FUNDS ON BASIS OF SHARPE RATIO

ORIGINAL ASSET ALLOCATION FOR KOTAK 30 GROWTH SCHEME

RESULTS OF SHARPE OPTIMISATION FOR KOTAK 30 GROWTH SCHEME

CONCLUSION

• SHARPE RATIO IS A BLUNT INSTRUMENT TO MEASURE RISK ADJUSTED RETURN

• IT PRESENTS A MORE COMPLETE PICTURE OF FUND PEFORMANCE THAN RAW RETURN

• IT HELPS INVESTORS EVALUATE RELATIVE SUCCESS OF COMPETING FUNDS FOLLOWING THE SAME BROAD INVESTMENT STRATEGIES

RECOMMENDATIONS

• WELL KNOWN PORTFOLIOS CAN HAVE IMPROPER DESIGNS TOO

• A GOOD FUND MANAGER SHOULD NOT RELY ON A SINGLE MEASURE FOR DESIGNING A PORTFOLIO

• FINALLY ,EVALUATION OF A FUND MANAGER SHOULD BE DONE MANY TIMES OVER DIFFERENT MARKET ENVIRONMENT

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“It is not the return on my investmentthat I am concerned about.

It is the return of my investment!”

– Will Rogers