Question

Your stockbroker has called to tell you about two stocks: Snap Inc. (SNP) and Twitter, Inc. (TWTR). She tells you that SNP is selling for $20.00 per share and that she expects the price in one year to be $40.00. TWTR is selling for $32.00 per share and she expects the price in one year to be $38.00. The expected return on SNP has a standard deviation of 25 percent, while the expected return on TWTR has a standard deviation of 15 percent. The market risk premium for the S&P 500 has averaged 6.0 percent. The beta for SNP is 1.76 and the beta for TWTR is .78. The 10-year Treasury bond rate is currently 1.00%. Neither SNP nor TWTR pays a cash dividend.

Required:

1. Determine the probability for each stock that you would earn a negative return.

2. Determine the probability for each stock that you would earn more than your required rate of return.

3. Explain why you would or would not buy either or both of the two stocks.

Answer 1

Answer:

Given that,

Your stockbroker has called to tell you about two stocks: Snap Inc. (SNP) and Twitter, Inc. (TWTR).

She tells you that SNP is selling for $20.00 per share and that she expects the price in one year to be $40.00.

TWTR is selling for $32.00 per share and she expects the price in one year to be $38.00.

The expected return on SNP has a standard deviation of 25 percent, while the expected return on TWTR has a standard deviation of 15 percent.

The market risk premium for the S&P 500 has averaged 6.0 percent. The beta for SNP is 1.76 and the beta for TWTR is 0.78.

The 10-year Treasury bond rate is currently 1.00%.

Neither SNP nor TWTR pays a cash dividend.

(a).

Determine the probability for each stock that you would earn a negative return:

The probability of each stock would earn a negative return is, We know that returns on a stock follow a normal distribution.

Let us assume that the Mean return on both of the stocks follows the CAPM model of return.

Expected Return on SNP (ESNP = Rt + BSNP( Rm - Rt)

Rt = Return on Risk-Free Treasury bonds,

BSNP= Beta of SNP Stock, Rm = Return of Market portfolio.

= 1+1.76 (6-1)

= 9.8 %,

Likewise Expected return on TWTR= 1+0.78 (6-1) = 4.9% as the returns on both the stocks will follow Normal distribution, the probability of them ending up with negative returns can be calculated by calculating the Z value below 0.

Where X = expected rate and = average return , = standard deviation

=(0-0.098)/0.25

=-0.392

For Z value of -0.392, look up for Z- table for negative values = 0.34753, Probability of getting negative returns for SNP= 0.34753.

Likewise, Z for TWTR = (0-0.049)/0.15 = -0.32667.

Z value = 0.37196 ,

Probability of getting negative returns for TWTR =0.37196.

We can observe that TWTR is having a higher probability of getting a negative return, that is because its standard deviation is low, reflecting more volatility in the stock.

(b).

Determine the probability for each stock that you would earn more than your required rate of return:

Probability of each stock earning more than the required rate of return.

Just like we calculated the probability of getting a return from 0 to expected return,

Probability of a stock earning more than expected return can be calculated by simply calculating (1- the probability of making 0 to the expected return.).

(c).

Explain why you would or would not buy either or both of the two stocks:

Expected return on TWTR= (38-32)/32 = 18.75%

Expected return on SNP = (40-20)/20 = 100%.

Both the stocks are expected to return higher than the CAPM expected returns, I would invest in the stocks.