Question

Consider the following historical performance data for two different portfolios, the Standard and Poor’s 500, and the 90-day T-bill.

Investment	Average Rate of		Standard
Vehicle	Return		Deviation		Beta	R2
Fund 1	26.80	%	21.42	%	1.427	0.739
Fund 2	13.52		14.30		0.944	0.722
S&P 500	15.90		12.80
90-day T-bill	6.20		0.60

1. Calculate the Fama overall performance measure for both funds. Round your answers to two decimal places.

   Overall performance (Fund 1): %

   Overall performance (Fund 2): %

2. What is the return to risk for both funds? Do not round intermediate calculations. Round your answers to two decimal places.

   Return to risk (Fund 1): %

   Return to risk (Fund 2): %

3. For both funds, compute the measures of (1) selectivity, (2) diversification, and (3) net selectivity. Do not round intermediate calculations. Round your answers to two decimal places. Use a minus sign to enter negative values, if any.

   	Selectivity		Diversification		Net selectivity
   Fund 1		%		%		%
   Fund 2		%		%		%

Answer 1

A)

Overall performance measure for fund1= excess return - risk free rate= 26.8-6.2= 20.6%

Overall performance measure for fund2= excess return - risk free rate= 13.52-6.2=7.32%

B)

Return to risk for Fund1 & 2

Return to risk for fund 1= beta*(market return- rsk free rate) = 1.427(0.159 - 0.062)= 13.84%

Return to risk for fund 2= beta*(market return- rsk free rate) = 0.944(0.159 - 0.062)= 9.156%

C)

Selectivity = Excess Portfolio Return or overall performance measure - required return for risk

Selectivity1= 20.6-13.84= 6.76%

Selectivity2= 7.32-9.156= -1.836%

DIversification

Diversification = Return for total risk – Expected Return

Expected return 1= Risk free rate + beta*(market return- rsk free rate) = 0.062 + 1.427(0.159 - 0.062)= 0.2004 or 20.04%

Expected return 2= Risk free rate + beta*(market return- rsk free rate) = 0.062 + 0.944(0.159 - 0.062)= 0.1535 or 15.35%

Return for total risk = Risk free rate + Ratio of total risk (Market return – Risk free rate)

Ratio of total risk1 = Standard deviation of 1/ stadard deviation of market

Ratio of total risk2 = Standard deviation of 2/ stadard deviation of market

Return for total risk1= 0.062+(21.42/12.8)(0.159 - 0.062)= 22.43%

Return for total risk2= 0.062+(14.30/12.8)(0.159 - 0.062)= 17.03%

Diversificaion1= 22.43-20.04= 2.39%

Diversification2= 17.03-15.35= 1.68%

net selectivity

Net Selectivity = Selectivity – Diversification

Net selectivity1= 6.76-2.39= 4.37%

Net selectivity2= -1.38-1.68= -3.06%