The following information has been collected for the returns of the OPop Corporation and the market portfolio: The covariance of the returns is 567%%. Calculate OPop's market beta.

Question

The following information has been collected for the returns of the OPop Corporation and the market portfolio:  The covariance of the returns is 567%%. Calculate OPop's market beta.

Quizplus · Accepted Answer

Market beta is defined as the covariance between the returns of an asset and the returns of the market divided by the variance of the returns of the market. 
Market beta = Covariance of the returns / Variance of the returns of the market
In this case, we are given the covariance of the returns between OPop Corporation and the market portfolio, which is 567%. However, we are not given the variance of the returns of the market, so we cannot directly calculate the market beta. 
Therefore, we need to use the information provided in the answers to find the market beta. 
We can see that the answer choices provide different values for the market beta. We want to choose the value that gives us a covariance of 567%. 
If we choose a beta that is too high, then the covariance will also be high, which means we will overshoot the 567% target. 
If we choose a beta that is too low, then the covariance will also be too low, which means we will undershoot the 567% target. 
Therefore, we want to choose the value that is closest to 567%. 
Looking at the answer choices, we can see that choice B) 1.4 gives us the closest value to 567%. 
Therefore, the answer is B) 1.4. To calculate market beta, we need to use the formula: 
Market beta = Covariance of OPop returns and market returns / Variance of market returns

We are given the covariance of the returns (567%) but we don't have the variance of the market returns. However, we do know that the market portfolio has a beta of 1.0 by definition. And beta is the covariance of the market returns with asset returns (in this case, OPop) divided by the variance of the market returns.

So, we can write: 
1.0 = Covariance of OPop returns and market returns / Variance of market returns

Solving for the variance of the market returns gives us: 
Variance of market returns = Covariance of OPop returns and market returns

Therefore, OPop's market beta is equal to the covariance of OPop returns and market returns (567%) divided by the variance of market returns (also 567%), which simplifies to 1.0.

Since we know the market has a beta of 1.0, OPop's market beta must also be 1.0. So, none of the answer choices are correct.

The Following Information Has Been Collected for the Returns of the OPop