Question

Q1: what does the efficient frontier represents?

Q2: how do we estimate the return and standard deviation of a newly built portfolio from analyzing the stocks in that portfolio?

Q3: in the regression equation, what is meant by a regression that has an R-square with 0.95 and how does it compare with a regression with a R-square of 0.30?

Q4: why do we use adjusted beta?

Q5: what is the information ratio and why do we use it?

Answer 1

1. Efficient frontier represents the portfolios which have the highest returns for a given level of risk. Or, it is the portfolio with the lowest level of risk for a given level of return. All the portfolios lying below this frontier are sub-optimal with lower returns for the given level of risk. Further, the frontier is curved due to the diminishing marginal returns per unit of additional risk.

2. Expected return of a newly built portfolio is the weighted average of the expected return of each of its stocks constituting the portfolio.

R(Portfolio) = W1* R1 + W2 *R2 +W3 * R3 + ........

where, W1, W2, W3 are the respective weights of individual stocks in portfolio

and, R1, R2, R3 are their respective returns.

Standard deviation of a newly built portfolio is calculated as:

(Standard deviation of portfolio)^2 = [R1 - R(Portfolio)]^2 + [R2 - R(Portfolio)]^2 + [R3 - R(Portfolio)]^2 + ........

(Standard deviation of portfolio) = {[R1 - R(Portfolio)]^2 + [R2 - R(Portfolio)]^2 + [R3 - R(Portfolio)]^2 + ........} ^(1/2)

3. R-square is the coefficient of determination which determines the closeness of fitted data for the regression model. So, regression with R-square with 0.95 will be a better fit compared to a regression with a R-square of 0.30. The low r-square value of 0.30 is a bad sign for predictive models.

4. Betas can exhibit mean reverting properties over a longer span of time and those significantly above 1 may eventually decline whereas betas below 1 may revert towards 1. So, analysts apply models to create an adjustment calculation for the historical beta and this adjusted beta is then used to determine the expected return for the stock.

5. Information ratio measures the rate of return of a portfolio against a benchmark equity index. Investors use this ratio to determine the excess returns per unit of risk. We can analyse the efficiency of fund manager in generating superior risk adjusted performance with respect to benchmark index.