MSF Assessment Exam FSU Questions
& Answers
If stock returns are normally distributed, they can be completely defined or
characterized by what statistical measures? - ANSWER- Mean
- Standard Deviation
In estimating statistical tests of significance, if you suspect your data are non-normal,
you might choose to use non-parametric tests because they do not assume normality.
What are some types/examples of these non-parametric tests? - ANSWER- Mann-
Whitney U Test
- Wilcoxon Ranked Sum Test
- Sign Test
In a time-series regression in which the y-variable is the excess return of a mutual fund
and the x-variable is the excess return on a market index, which result/measure would
suggest that the fund manager outperformed on a risk-adjusted basis (i.e., "beat the
market") in a statistical sense? - ANSWER- There is alpha
- An alpha greater than 0 means the mutual fund outperformed the market index after
adjusting for volatility.
You collect a sample of stock returns for 100 firms. For each firm you collect monthly
stock returns over the past 12 months. The resulting dataset can be best described as
_________ data. - ANSWER- Panel Data:
- Time-Series
- Cross-Sectional
You are doing an event study on firms that announce earnings. Let's assume that for
each sample firm, you would like to calculate the abnormal stock return on the event
date. You decide to use the S&P 500 as your estimate of the normal or expected return.
Thus, for each sample firm, your measure of abnormal return on the event date would
equal __________. - ANSWER- Daily Return(stock) - Daily Return(S&P 500):
- (Realized - Expected)
In excel, the output for a regression analysis includes___________. - ANSWER· R-
squared value: The percentage of variation in the dependent variable explained by the
independent variable(s)
· Adjusted R-squared value: Takes into account the number of independent variables in
the model
· ANOVA table: Overall significance of the regression model, including F-statistic and p-
value
, · Coefficients table: Estimates of the regression coefficients, including intercept and
coefficients for each independent variable, with standard error, t-value, and p-value
· Residuals and fitted values: Differences between actual and predicted values of the
dependent variable, and predicted values of the dependent variable based on the
regression model
·Regression equation: Equation for the regression line that can be used to predict the
value of the dependent variable based on the values of the independent variable(s)
An actively managed equity fund has an expected rate of return of 10% and a standard
deviation of 22%. T-bills currently offer a risk-free rate of return of 3%. Assume an
investor has a utility function of the form *U = E(r) ‒ ½Aσ2*. Which asset allocation
(percentage of T-bills and active fund) will this investor prefer if they have a risk-
aversion coefficient of 4.0? - ANSWER*To determine the optimal asset allocation for the
investor, we need to find the combination of T-bills and the actively managed equity
fund that maximizes the investor's expected utility.
Let x be the proportion of the portfolio invested in the actively managed equity fund, and
(1-x) be the proportion invested in T-bills.
The expected return of the portfolio can be calculated as:
E(r) = x * 10% + (1-x) * 3% = 3% + 7x%
The portfolio's standard deviation can be calculated as:
σ = x * 22%
Using the given utility function, the investor's expected utility can be calculated as:
U = E(r) - 0.5 * A * σ^2
= (3% + 7x%) - 0.5 * 4.0 * (x * 22%)^2
= (3% + 7x%) - 0.44x^2
To maximize the investor's expected utility, we need to find the value of x that
maximizes U. To do this, we can take the derivative of U with respect to x and set it
equal to zero:
dU/dx = 7 - 0.44 * 2x = 0
x = 7/0.88 = 7.95
Therefore, the investor should allocate approximately 7.95% of the portfolio to T-bills
and the remaining 92.05% to the actively managed equity fund to maximize their
expected utility.
An airline expects to purchase several million gallons of jet fuel eight months from now.
They have chosen to hedge this exposure with heating oil futures. Assume the
correlation of jet fuel and heating oil futures is 0.86. Assume also that the standard
deviation of jet fuel prices is 0.30 and the standard deviation of heating oil futures prices
is 0.36. What is the minimum-variance hedge ratio? - ANSWERcorrelation * stdev (spot)
/ stdev (futures)
= .86 * .30 / .36 = 0.72
The value of an American call option on a dividend paying stock _____(1)_____ with
strike price, _____(2)_____ with stock price, _____(3)_____ with the stock's volatility,
and _____(4)_____ with the value of future dividends. - ANSWER1. Negatively
correlated; decreases
& Answers
If stock returns are normally distributed, they can be completely defined or
characterized by what statistical measures? - ANSWER- Mean
- Standard Deviation
In estimating statistical tests of significance, if you suspect your data are non-normal,
you might choose to use non-parametric tests because they do not assume normality.
What are some types/examples of these non-parametric tests? - ANSWER- Mann-
Whitney U Test
- Wilcoxon Ranked Sum Test
- Sign Test
In a time-series regression in which the y-variable is the excess return of a mutual fund
and the x-variable is the excess return on a market index, which result/measure would
suggest that the fund manager outperformed on a risk-adjusted basis (i.e., "beat the
market") in a statistical sense? - ANSWER- There is alpha
- An alpha greater than 0 means the mutual fund outperformed the market index after
adjusting for volatility.
You collect a sample of stock returns for 100 firms. For each firm you collect monthly
stock returns over the past 12 months. The resulting dataset can be best described as
_________ data. - ANSWER- Panel Data:
- Time-Series
- Cross-Sectional
You are doing an event study on firms that announce earnings. Let's assume that for
each sample firm, you would like to calculate the abnormal stock return on the event
date. You decide to use the S&P 500 as your estimate of the normal or expected return.
Thus, for each sample firm, your measure of abnormal return on the event date would
equal __________. - ANSWER- Daily Return(stock) - Daily Return(S&P 500):
- (Realized - Expected)
In excel, the output for a regression analysis includes___________. - ANSWER· R-
squared value: The percentage of variation in the dependent variable explained by the
independent variable(s)
· Adjusted R-squared value: Takes into account the number of independent variables in
the model
· ANOVA table: Overall significance of the regression model, including F-statistic and p-
value
, · Coefficients table: Estimates of the regression coefficients, including intercept and
coefficients for each independent variable, with standard error, t-value, and p-value
· Residuals and fitted values: Differences between actual and predicted values of the
dependent variable, and predicted values of the dependent variable based on the
regression model
·Regression equation: Equation for the regression line that can be used to predict the
value of the dependent variable based on the values of the independent variable(s)
An actively managed equity fund has an expected rate of return of 10% and a standard
deviation of 22%. T-bills currently offer a risk-free rate of return of 3%. Assume an
investor has a utility function of the form *U = E(r) ‒ ½Aσ2*. Which asset allocation
(percentage of T-bills and active fund) will this investor prefer if they have a risk-
aversion coefficient of 4.0? - ANSWER*To determine the optimal asset allocation for the
investor, we need to find the combination of T-bills and the actively managed equity
fund that maximizes the investor's expected utility.
Let x be the proportion of the portfolio invested in the actively managed equity fund, and
(1-x) be the proportion invested in T-bills.
The expected return of the portfolio can be calculated as:
E(r) = x * 10% + (1-x) * 3% = 3% + 7x%
The portfolio's standard deviation can be calculated as:
σ = x * 22%
Using the given utility function, the investor's expected utility can be calculated as:
U = E(r) - 0.5 * A * σ^2
= (3% + 7x%) - 0.5 * 4.0 * (x * 22%)^2
= (3% + 7x%) - 0.44x^2
To maximize the investor's expected utility, we need to find the value of x that
maximizes U. To do this, we can take the derivative of U with respect to x and set it
equal to zero:
dU/dx = 7 - 0.44 * 2x = 0
x = 7/0.88 = 7.95
Therefore, the investor should allocate approximately 7.95% of the portfolio to T-bills
and the remaining 92.05% to the actively managed equity fund to maximize their
expected utility.
An airline expects to purchase several million gallons of jet fuel eight months from now.
They have chosen to hedge this exposure with heating oil futures. Assume the
correlation of jet fuel and heating oil futures is 0.86. Assume also that the standard
deviation of jet fuel prices is 0.30 and the standard deviation of heating oil futures prices
is 0.36. What is the minimum-variance hedge ratio? - ANSWERcorrelation * stdev (spot)
/ stdev (futures)
= .86 * .30 / .36 = 0.72
The value of an American call option on a dividend paying stock _____(1)_____ with
strike price, _____(2)_____ with stock price, _____(3)_____ with the stock's volatility,
and _____(4)_____ with the value of future dividends. - ANSWER1. Negatively
correlated; decreases
