Question

Stock Albatross has a risk-premium of 7 and a beta of 1.2. Stock Herring has a risk-premium of 6 and a beta of 0.9. Based on these numbers, you should prefer:

Herring because the reward-to-risk ratio is larger.

We need to know the variance before we can pick between the two.

Herring because the reward-to-risk ratio is smaller.

Albatross because the reward-to-risk ratio is smaller.

Albatross because we always want the stock with the highest expected return.

My calculation for the above question is

Assume Risk free rate as 5%

Expected Return for Albatross – 5% + 7x1.2 = 5% + 8.4% = 13.4%

Expected return for Herring – 5% + 6x0.9 = 5% + 5.4% = 10.4%

Reward-to-risk ratio of Albatross = expected return – risk free rate /beta = 0.134 – 0.05/1.2=0.07 = 7%

Reward-to-risk ratio of Herring = 0.104 – 0.05/0.9=0.06 = 6%

According to this we should prefer Albatross because the reward-to-risk ratio is higher but I could not find the option in the question.

Is my understanding right? Please help me with this.

Answer 1

What you have derivied is market premium. This is quest obvious because the way you have derived the expected return , it will obviously give you back risk premium.

Expected return = Risk free + Beta ( Risk free - market return) = Risk free + Beta x risk premium

Risk premium = ( Expected return - risk free ) / Beta --------------> Which you have derived and come back to square one.

My explanation:

Risk premium ( Market return over risk free rate) is you reward and beta measures the volatility or the risk. Since, Beta is calculated using variance of market return, we dont need to to get its variance once again.

Now see below calculation

Risk -reward ratio = Risk premium / risk ( systematic)

Stock	Risk Premium	Risk	Reward-Risk ratio
Albatross	0.07	1.2	0.0583
Herring	0.06	0.09	0.6667

Hnece stock herring is better