Question

AS A PORTFOLIO MANAGER , ASSUME THE FOLLOWING INFORMATION:

THE BETA OF YOUR PORTFOLIO 1.2

YOUR PERFORMANCE IS EXACTLY ON TARGET WITH THE SML DATA UNDER CONDITION 1

ASSUME THE TRUE SML DATA IS GIVEN UNDER CONDITION 2

CONDITION 1

RFR 0.04

RM(PROXY) 0.1

CONDITION 2

RK 0.05

RM(TRUE) 0.12

HOW MUCH DOES YOUR PERFORMANCE DIFFER FROM THE TRUE SML?

Answer 1

Under Condition-1

Stock Return Ri = Rf + b*(Rm-Rf)

Ri = Stock Return

Rf = Risk-Free Rate of Return

b = Beta of Instrument

Rm = Market Rate of Return

Hence from the data provided in condition -1:

Ri = 0.04 + (1.2)*(0.1.- 0.04) = 0.04+1.2*0.06

Ri = 0.04 + 0.072 = 0.112 or 11.2%

Under Condition -2

The Market Return is given as 0.12

The Required Return of Portfolio then is:

Ri' = 0.04 + 1.2*(0.12-0.04)

Ri' = 0.04 + 1.2*(0.08) = 0.04-0.096 = 0.136 or 13.6%

Thus the difference of performance from true SML data is (11.2 -13.6)% = 2.4% lesser.