Free PRMIA 8006 Practice Exam with Questions & Answers | Set: 9

A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.

A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.

The Sharpe ratio is the ratio of excess returns to risk. Excess returns are measured as the returns over the risk-free rate, and risk is measured in terms of volatility, ie standard deviation. Two portfolios with identical Sharpe ratios will certainly have the same ratio of risk and return, though the absolute levels of the return and the risk may vary. Therefore Choice 'c' is the correct answer.

This question relates to the Black Scholes PDE (partial differential equation). The Black Scholes PDE is derived by combining the results of a stock price following a Weiner process with a mathematical result known as Ito's lemma and holds true for all derivatives whose prices depend upon S, the price of the underlying and upon t, which indicates time.

The derivation of the Black Scholes PDE is beyond the scope of the PRM syllabus (and also of the author of this question), but we need to know what it is. The PDE can be written as:

202.21.q1

Substituting , this can also be written as

202.21.e

202.21.q2

Therefore the first and the second equations are correct, and the other two are wrong. Choice 'c' is the correct answer.

You should know the PDE in case there is a numerical question about it. The two ways of writing it (as I and II above in the question) express the same relationship. The BSM formula itself for valuing a vanilla European option is based upon the PDE. Most other options are also valued using the fundamental relationship expressed in the PDE.

The Sharpe ratio does not require investors to be risk neutral, only that for a given level of returns they prefer less risk to more risk. (Risk neutral means that investors are indifferent to the level of risk, and are only driven by a desire to maximizing expected value, regardless of risk levels.)

The ability to borrow and lend any amounts of money at the risk free rate is a fundamental assumption for the rule that optimal portfolios will maximize the Sharpe ratio.

This rule also assumes that risk preferences are completely described by return and standard deviation of returns.

Therefore Choice 'd' is the correct answer as statements I and II are correct.

A money market security is one that is initially issued with a maturity of less than one year. Treasury bills are short-term government securities with maturities ranging from a few days to 52 weeks. Bills are sold at a discount from their face value, and do not carry a coupon. Treasury notes and treasury bonds are not money market instruments as they are issued for a maturity greater than a year. Treasury notes are issued with maturities of 2, 3, 5, 7, and 10 years and pay interest every six months. Treasury bonds pay interest every six months and mature in 30 years.

Commercial paper is issued by corporations to meet their short term funding needs and is a money market instrument. Bankers' acceptances are short term loans to corporations that are guaranteed by a bank.

Of the given list, since treasury notes are the only instrument that are not money market securities, Choice 'a' is the correct answer.

Since the stock is selling for $100 spot, its 3 month forward price for you would be $100*(1 + 6%*3/12) = $101.50. Since the forward is priced at $104, it is 'rich' compared to the spot and should be sold. A profitable trade would be to buy the spot and sell the forward.

Imagine you borrow $100 and buy the stock, and simultaneously sell the forward. At the end of 3 months, you will receive $104 in return from the forward, and be obliged to return the initial $100 borrowed together with interest of $1.50 for the three months. You would make a riskless profit of $2.50 per share in three months. Thus Choice 'c' is the correct answer.

Note that the treasury yield is irrelevant, what matters is the rate at which you can finance the trade which is 6% per annum.