Question

Firm	Portfolio Weight	Volatility (Standard Deviation)	Correlation w/ Market Portfolio
A	0.25	14%	0.7
B	0.35	18%	0.6
C	0.40	15%	0.5

The volatility of the market portfolio is 10%, the expected return on the market is 12%, and the risk-free rate of interest is 4%.

1) Calculate the beta for each stock.

2) Calculate the beta for the portfolio of the three stocks.

3) Calculate the beta for the market.

4) Calculate the expected return for each stock.

5) Calculate the expected return for the portfolio of the three stocks.

Answer 1

Part 1:

Sec A:

Particulars	Values
SD of Security	14%
SD of Market	10%
Correlation ( Sec, Mkt)	0.7

Beta = [ SD of Sec / SD of Market ] * Correlation ( Sec, Mkt )
= [ 14 % / 10 % ] * 0.7
= [ 140 % ] * 0.7
= 0.98 Times

Sec B:

Particulars	Values
SD of Security	18%
SD of Market	10%
Correlation ( Sec, Mkt)	0.6

Beta = [ SD of Sec / SD of Market ] * Correlation ( Sec, Mkt )
= [ 18 % / 10 % ] * 0.6
= [ 180 % ] * 0.6
= 1.08 Times

Sec C:

Particulars	Values
SD of Security	15%
SD of Market	10%
Correlation ( Sec, Mkt)	0.5

Beta = [ SD of Sec / SD of Market ] * Correlation ( Sec, Mkt )
= [ 15 % / 10 % ] * 0.5
= [ 150 % ] * 0.5
= 0.75 Times

Part 2:

Portfolio Beta is weighted Avg beta of securities in that portfolio

Security	Weights	Beta	Wtd Beta
A	0.2500	0.98	0.2450
B	0.3500	1.08	0.3780
C	0.4000	0.75	0.3000
Portfolio Beta			0.9230

Part 3:

Beta of Market is always 1

Part 4:

Beta Specifies Systematic Risk
Systematic risk specifies the How many times security return will deviate to market changes.
SML return considers the risk premium for Systematic risk alone.Where as CML return considers risk premium for Total risk.
Beta of market is "1".

Stock A:

Particulars	Amount
Risk Free Rate	4.0%
Market Return	12.0%
Beta	0.9800
Risk Premium ( Rm - Rf)	8.00%

Expected Return = Rf + Beta ( Rm - Rf )
= 4 % + 0.98 ( 8 % )
= 4 % + ( 7.84 % )
= 11.84 %

Stock B:

Particulars	Amount
Risk Free Rate	4.0%
Market Return	12.0%
Beta	1.0800
Risk Premium ( Rm - Rf)	8.00%

Expected Return = Rf + Beta ( Rm - Rf )
= 4 % + 1.08 ( 8 % )
= 4 % + ( 8.64 % )
= 12.64 %

Stock C:

Particulars	Amount
Risk Free Rate	4.0%
Market Return	12.0%
Beta	0.7500
Risk Premium ( Rm - Rf)	8.00%

Expected Return = Rf + Beta ( Rm - Rf )
= 4 % + 0.75 ( 8 % )
= 4 % + ( 6 % )
= 10 %

Part 5:

Particulars	Amount
Risk Free Rate	4.0%
Market Return	12.0%
Beta	0.9230
Risk Premium ( Rm - Rf)	8.00%

Expected Return = Rf + Beta ( Rm - Rf )
= 4 % + 0.923 ( 8 % )
= 4 % + ( 7.38 % )
= 11.38 %