Question 1
Suppose that u=1.5, d=0.5, r=0.10, S=120. What is the price of a put option struck at K=0?
a. 150.00
b. 100.00
c. 120.00
d. 90.909
e. None of the above

Question 2
Consider an at-the-money call option and an at-the-money put option.
Both options are European. They have different Black-Scholes implied volatilities [i.e., the
Black-Sholes formula for option prices implies different levels of stock’s volatility for the price
of the put and the price of the call]. This means , that
a. The put-call parity is violated for these two options;
b. there is an arbitrage opportunity ;
c. The put-call parity implies the Black-Sholes formula ;
d. All three above;
e. None of the above.

Question 3
Consider an asset allocation problem with a single risky asset with expected return and volatility σ
and assume the risk-free rate is r. Let rp denote the risky return on a portfolio consisting of w% of
your wealth in the risky asset and the remainder in the risk free asset.
The Sharpe ratio of a
a. leveraged portfolio is greater than the Sharpe ratio of an unleveraged portfolio
b. leveraged portfolio is less than the Sharpe ratio of an unleveraged portfolio
c. leveraged portfolio is the same as the Sharpe ratio of an unleveraged portfolio;
d. We do not have enough information to answer this question;
e. None of the above

Question 4
Suppose you have a portfolio problem with 10 assets. If you add another asset, the slope of the
tangency portfolio
a. increases or at least stays the same
b. decreases or at least stays the same
c. could do either depending on covariance of the new asset with the other assets;
d. We do not have enough information to answer this question;
e. None of the above.