Sharpe Ratio in Investment Analysis
Learn about Sharpe Ratio, a key financial metric for evaluating portfolio performance based on risk-adjusted returns. Discover how to compute Sharpe Ratio from daily and monthly returns, along with examples and practical applications in investment analysis.
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Sharpe Ratio J.-S. Roger Jang ( ) MIR Lab, CSIE Dept. National Taiwan University jang@mirlab.org, http://mirlab.org/jang 2025/4/4
Sharpe Ratio (SR) Definition ?? =? ?0 Bank deposit interest rate ? ?: mean yearly return rate, ?0: risk-free return rate, ?: standard deviation of yearly return rate ? is also known as volatility or risk Use of Sharpe ratio A way to evaluate a long-term portfolio Assume ?0=0 The return rate when the volatility is 1% Examples SR=0.5 Assume ?0=0 Expected return = 0.5% if the volatility is 1% Expected return = 5% if the volatility is 10% 2/
Examples of Sharpe Ratio Comparison of Sharpe ratios of two portfolios https://rich01.com/what-sharpe-ratio/ 3/
Compute SR from Daily Return Time resolution of yearly ?? and ?? too low How to compute ?? and ?? based on daily ?? and ??? ????? ?????? =????? ? ??? ???? ????????? ? ??? ???? ????????? ? ??? ???? ? = ?1+ ?2+ + ?252 ??= 252 ?? 2= 252?? 252: Average trading days per year ?: ? = ?? and ? = ?? ??: ? = ?? and ? = ?? 2 ?? ??0 252 ?? ?? ?? ??0 ?? 252?? ??0 252?? ???= = 252 = ??? 252 = Similarly, to compute SR from monthly return: ???= ??? 12 4/ Source: https://www.realvantage.co/insights/what-is-sharpe-ratio/
Hint Assumptions ?1,?2and X are independent. They have the same ? and and ?: ? = ?? and ? = ?? Different implications of the two equations ?1= ?1+ ?2 ?2= 2? ?1and ?2have the same mean ??, but different variances: ??1 ??2 2= 2??2 2= 4??2 5/
Example Assume the five days prices of a stock are [6 8 7 9 8] and the risk-free return is 1%, what is the corresponding Sharpe ratio? Solution: return=[2/6, -1/8, 2/7, -1/9]; mu=0.0957 sigma=0.2477 SRd=(mu-0.01/252)/sigma=0.3863 SRy=sqrt(252)* SRd=6.1330 6/
