# tere bin

Topics: Investment, Modern portfolio theory, Sharpe ratio Pages: 6 (562 words) Published: February 24, 2014
SECURITY ANALYSIS AND PORTFOLIO
MANAGEMENT
SHARPEN INDEX MODEL
By Jissmol George

SHARPEN INDEX MODEL

The Sharpe index is a measure in which the performance
of portfolio in a given period of time is measured.
In Sharpe index, three things must be known:
 the portfolio return,
 the risk free rate of return - use the average return
(over the given period of time).
 the standard deviation of the portfolio – it is
measure the systematic risk of the portfolio.
The ratio describes how much excess return you are
receiving for the extra volatility that you endure for
holding a riskier asset
Properly compensated for the additional risk you take for
not holding a risk-free asset

CONDITIONS

Return (rp):

The returns measured can be of any frequency (i.e.
daily, weekly, monthly or annually), as long as they are
normally distributed, as the returns can always be
annualized.
Herein lies the underlying weakness of the ratio - not all
asset returns are normally distributed.

Risk-Free Rate of Return (rf ):

The risk-free rate of return is used to see if the investors are properly compensated for the additional risk taken
on with the risky asset.
Traditionally, the risk-free rate of return is the shortest
dated government T-bill .
While this type of security will have the least volatility

Standard Deviation (StdDev(x)):
 First calculate the excess return from subtracting
the return of the risky asset from the risk-free rate
of return,
 Next need to divide this by the standard
deviation of the risky asset being measured.
 As mentioned above, the higher the number,
the better the investment looks from a risk/return
perspective.

CALCULATION

The Sharpe index is computed by dividing the risk premium of the portfolio by its standard deviation or total risk.

Symbolically, the Sharpe index is presented as:

Here,

= portfolio rate of return f

rf = risk free rate of return

σ = standard deviation.

The higher the Sharpe measure indicates a better performance because each unit of total risk (standard deviation) is rewarded with greater excess return.

Demonstration with example

Suppose that the 10-year annual return for the S&P
500 (market portfolio) is 18%, while the average
annual return on Treasury bills (a good proxy for the
risk-free rate) is 5%. Then assume you are evaluating
three distinct portfolio managers with the following
10-year results:
Manager

Manager X
Manager Y
Manager Z

Annual Return

Portfolio Standard
Deviation

14%

0.11

17%

0.20

19%

0.27

SOLUTION
S(market) = (.10-.05)/.18 = .278
S(manager X) = (.14-.05)/.11 = .818
S(manager Y) = (.17-.05)/.20 = .600
S(manager Z) = (.19-.05)/.27 = .519
Once again, we find that the best portfolio is not
necessarily the one with the highest return. Instead, it's
the one with the most superior risk-adjusted return, or in
this case the fund headed by manager X.

CONCLUSION

The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the performance of a portfolio.

The ratio helps to make the performance of one portfolio
comparable to that of another portfolio by making an adjustment for risk.
A ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent.
The Sharpe ratio evaluates the portfolio manager on the basis of both rate of return and diversification (as it considers total portfolio risk as measured by standard deviation in its denominator).

Therefore, the Sharpe ratio is more appropriate for well diversified portfolios, because it more accurately takes into account the risks of the portfolio.

THANK YOU