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What is Sharpe Ratio?

Sharpe Ratio: 
It is derived by William F. Sharpe in 1966. It measure the risk adjusted return of a portfolio.  It helps to determine the efficiency of an investment portfolio. The ratio measure the excess return earned by investors by investing in a risky investment. The higher ratio indicates that the investment portfolio gives better return to its holder.If volatility of an expected return is higher than the Sharpe ratio will be low.

Formula:
Sharpe ratio = (Rp – Rf) / σp

Where,
Rp = Expected return of a portfolio
Rf = Risk free rate
σp = Standard deviation of a portfolio

Advantages of Sharpe ratio:
·         It is simple and easy to calculate.
·         It measure the risk adjusted return of a portfolio.

Disadvantages of Sharpe ratio:
·         It does not differentiate between systematic risk and unsystematic risk.
·         It does not give accurate result because it based on historical data.
·         The risk of the portfolio is measure by only standard deviation which does not provide correct result for all type of funds like hedge funds.

Example: Calculate Sharpe ratio with the help of given information:
·         The expected return of stock A is 9% and risk free rate of return is 2%.
·         The standard deviation of stock A is 35%.

Solution:
Sharpe ratio = (Rp – Rf) / σp
= 9 – 2 / 35
= 0.2%

Example: Mr. X wants to invest his money in stock but he does not know which stock give better return after considering the market risk. With the help of following information find out which investment is better?
·         Suppose there is a two stock A and B. The expected return of stock A and B are 8% and 7.5% respectively.
·         The standard deviation of both the stocks is 5.7%.
·         The risk free rate of return of stock B and A are 3% and 2% respectively.

Solution: Sharpe ratio of stock A:
Sharpe ratio = (Rp – Rf) / σp
= 8 – 2 / 5.7
= 1.05%
Sharpe ratio of stock B:
Sharpe ratio = (Rp – Rf) / σp
= 7.5 – 3 / 5.7
= 0.78%                      
A Sharpe ratio of stock A is 1.05% which is more than the Stock B ratio that is 0.78%. So, it shows that the stock A gives more return in comparison to risk associated with the stock.

Example: Mr. Y has invested his savings in stock A and he wants to determine the average return he got after adjusting the risk or volatility. Find out how risky that investment for Mr. Y with the help of Sharpe ratio.
·         The expected return of stock MN is 12.3% and the risk free rate is 3.5%.
·         The Sharpe ratio is 1/3 of expected return.

Solution: Sharpe ratio = 1/3 *12.3 = 4.1
Sharpe ratio = (Rp – Rf) / σp
4.1 = 12.3 – 3.5 / σp
σp = 8.8 / 4.1
= 2.15%
Stock A is 2.15% risky and it also shows that if the asset is less risky than the average adjusted return will be high.


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