Question

Use the following information to evaluate whether or not you should buy stock A.

                                Stock A                                                                                 S&P 500

                Probability                          Return                                  Probability          Return

                    0.1                                         -100%                                      0.3                     -30%

                    0.2                                          -10%                                       0.4                         15%

                    0.6                                          18%                                        0.3                         40%

                    0.1                                         130%

The current yield on the 10-year Treasury Note (risk-free rate) is 3.3%. The correlation between Stock A and the market is 0.53.   Hint One – Remember that the S&P 500 represents the market and that you can use the two probability distributions above to get the expected return and standard deviation for both Stock A and for the market (round calculations to 2 decimal places in percentage terms). Hint Two – You will use the SML to get the required return and you will need to calculate beta from the data provided (round beta to two decimal places).

Answer 1

Step1: Calculation of Expected Return and standard deviation

-Stock A

Probability(P)	Rate of Return(%)	Probability*Rate of Return	Deviation (D)	PD2
0.1	-100	-10.00	-111.8000	1249.92
0.2	-10	-2.00	-21.8000	95.05
0.6	18	10.80	6.2000	23.06
0.1	130	13.00	118.2000	1397.12

Expected Return = 11.80% (-10-2+10.8+13)

Variance = 2765.16

Standard Deviation (SD_A) = Variance

= 2765.16

=52.58%

-Market

Probability(P)	Rate of Return(%)	Probability*Rate of Return	Deviation (D)	PD2
0.3	-30	-9.00	-39.00	456.30
0.4	15	6.00	6.00	14.40
0.3	40	12.00	31.00	288.30

Expected Return = 9.00% (-9+6+12)

Variance = 759

Standard Deviation (SD_M) = 759

= 27.55%

Step2: Calculation of Beta

Beta = (SD_A*Correlation) / SD_M

= (.5258*.53) / .2755

= 1.01

Step 3: Calculation of required return under Capital asset Pricing Model(CAPM)

Required Return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return (here 3.3%)

b – Beta (here 1.01)

Rm – Expected return on market portfolio (here 9%)

Required Return = Rf + b ( Rm – Rf )

= 3.3 + 1.01 (9 - 3.3)

= 9.06%

Analysis : Since expected return (11.80%) is greater than the required return under CAPM (9.06%) . stock A is undevalued, should buy.