Question

Suppose that the S&P 500, with a beta of 1.0, has an expected return of 16% and T-bills provide a risk-free return of 7%.

a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) 0.25; (iii) 0.50; (iv) 0.75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter the value of Expected return as a percentage rounded to 2 decimal places and value of Beta rounded to 2 decimal places.)

b. How does expected return vary with beta? (Do not round intermediate calculations.)

(The expected Return _____ by _____ % for a one unit increase in beta)

Answer 1

a. i)Expected of Return of Portfolio =Weight of S&P *Return of S&P +Weight of T-bills *Return of T-bills =0%*16%+100%*7% =7%
Beta of risk free rate =0
Beta of Portfolio =Weight of S&P*Beta of S&P+Weight of T-bill*Beta of t-bill =0%*1+100%*0=0
ii) Expected of Return of Portfolio =Weight of S&P *Return of S&P +Weight of T-bills *Return of T-bills =0.25*16%+0.75*7% =0.0925
Beta of risk free rate =0
Beta of Portfolio =Weight of S&P*Beta of S&P+Weight of T-bill*Beta of t-bill =0.25*1+0.75*0=0.25
iii) Expected of Return of Portfolio =Weight of S&P *Return of S&P +Weight of T-bills *Return of T-bills =0.50*16%+0.50*7% =11.5%
Beta of risk free rate =0
Beta of Portfolio =Weight of S&P*Beta of S&P+Weight of T-bill*Beta of t-bill =0.50*1+0.50*0=0.5
iv)Expected of Return of Portfolio =Weight of S&P *Return of S&P +Weight of T-bills *Return of T-bills =0.75*16%+0.25*7% =13.75%
Beta of risk free rate =0
Beta of Portfolio =Weight of S&P*Beta of S&P+Weight of T-bill*Beta of t-bill =0.75*1+0.25*0=0.7
v) Expected of Return of Portfolio =Weight of S&P *Return of S&P +Weight of T-bills *Return of T-bills =1*16%+0*7% =16%
Beta of risk free rate =0
Beta of Portfolio =Weight of S&P*Beta of S&P+Weight of T-bill*Beta of t-bill =1*1+0*0=1

b..Expected return increases by Expected Return -Risk free rate =16%-7% =9%