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Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses…
Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data
You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…
The natural logarithm of x is:
Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?
Find the first-order Taylor approximation p(x) for the function: at the point .
I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is
I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?
Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:
What is the simplest form of this expression: log2(165/2)
In statistical hypothesis tests, 'Type I error' refers to the situation in which…
Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)
There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?
An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105
You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?
Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?
Every covariance matrix must be positive semi-definite. If it were not then: