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	26.20	%	20.34	%	1.307	0.764
Fund 2	13.36		14.40		0.907	0.719
S&P 500	14.78		12.90
90-day T-bill	5.50		0.40

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. 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		%		%		%

3. Explain the meaning of the net selectivity measure and how it helps you evaluate investor performance. Which fund had the best performance?

   The net selectivity is an unexplained portion of the excess -return OR risk Item 11 -Select-reduced by the cost of incomplete OR increased by the benefit from perfect Item 12 diversification. The higher the net selectivity the -Select-better OR worse Item 13 investor performance is. -Select-Fund 1 OR Fund 2 Item 14 had the best performance.

Answer 1

a)

Overall performance measure for fund1= excess return - risk free rate= 26.2-5.5= 21%

Overall performance measure for fund2= excess return - risk free rate= 13.36-5.5 = 7.86%

Return to risk for Fund1 & 2

Return to risk for fund 1= beta*(market return- rsk free rate) = 1.307(14.78% - 5.5%)= 12.13%

Return to risk for fund 2= beta*(market return- rsk free rate) = 0.907(14.78% - 5.5%)= 8.417%

b)

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

Selectivity1= 21-12.13= 8.87%

Selectivity2= 7.86-8.417= -0.557%

DIversification

Diversification = Return for total risk – Expected Return

Expected return 1= Risk free rate + beta*(market return- rsk free rate) = 5.5% + 1.307(14.78% - 5.5%)= 17.63%

Expected return 2= Risk free rate + beta*(market return- rsk free rate) = 5.5% + 0.907(14.78% - 5.5%)= 13.92%

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= 5.5% + (20.34/12.9)(14.78% - 5.5%)= 20.13%

Return for total risk2= 5.5% + (14.4/12.8)(14.78% - 5.5%)= 15.94%

Diversificaion1= 20.13-17.63= 2.5%

Diversification2= 15.94-13.92= 2.02%

net selectivity

Net Selectivity = Selectivity – Diversification

Net selectivity1= 8.87%-2.5%= 6.37%

Net selectivity2= -0.557%-2.02%= -2.557%

C) Net selectivity is the excess return earned by a fund or stock over and above the return that was expected out of it after considering for its total risk (Systematic and the remaining portion of unsystematic risk due to inefficient diversification). This is a measure of how well the fund manager was able to beat the market as to speak.

Since Fund 1 has higher net selectivity, it is the better performing fund.

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