PRMIA 8006 - Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

Since the 10 year rate has stayed the same, but the curve has gone from being flat to upward sloping, it means the shorter term interest rates have gone down. Recall that Macaulay duration is the PV of the payments received on a bond over its life weighted by the year each payment is received in. Also remember that a bond's current price is nothing but the summation of the different PVs of its various payments. It effectively gives the real average life of the bond - for example if a hypothetical (and impossible) bond derives half of its value from a payment today and the other half from a payment in 10 years, the investor can look at the average as being 5 years (0*50% + 10*50%). That is what is what we are calculating when deriving Macaulay duration.

In this case, a reduction in the near term interest rates increases the PV of the payments received prior to the payment at 10 years. This increases the value of the bond, and also increases the weightage of the earlier payments, decreasing the Macaulay duration (by shifting it closer to now and further behind from the maturity date).

The efficient markets hypothesis states that all known information is captured in the prices of a security. It does not explain the shape of the yield curve.

The expectations hypothesis, the LPT and the market segmentation theory are all attempts to explain the shape of the term structure of interest rates.

Therefore Choice 'c' is the correct answer as it does not explain the shape of the yield curve.

The optimal hedge ratio answers the question of how much of the hedge to buy to hedge a given position. If 103.11.e1 is the standard deviation of the asset to be hedged, and 103.11.e2 is the standard deviation the asset being used to hedge against price movements in x, then the minimum variance hedge ratio is given by the expression 103.11.e3. In this question, correlation = 0.00378/(6%*7%) = 0.9. The minimum variance hedge ratio is given by (6%/7%)*0.9 = 0.77

He should therefore hold 0.77 x $10m /$100k = 77 contracts.

[We can also do a direct covar based calculation for the min variance hedge ratio as follows:

103.11.a3

= 0.00378 / (0.07 * 0.07) = 0.7714]

A cash or nothing call is one that pays a fixed amount if the underlying exceeds a certain threshold, or nothing. An asset or nothing call is the same as the cash or nothing call except that instead of paying a fixed amount, it 'pays' the asset. Therefore the payoff profile of a long asset or nothing call has the same payoff as a long cash or nothing call and a long vanilla call.

This is best considered by building payoff diagrams which will show how the two positions are economically equivalent. Choice 'd' is the correct answer, and the rest are not.

Analytical methods are more 'efficient' than numerical methods in terms of computing power required, consistency of results and providing clarity on the inputs driving the results. Therefore 'efficient valuation' is not a reason to adopt numerical pricing methods over analytical methods.

It is much easier to incorporate changing stochastic volatility, discontinuous asset prices or other complex payoffs using numerical pricing methods. So these certainly represent good reasons to use numerical pricing methods for valuing exotics.

Therefore Choice 'b' is the correct answer.

It is important to note the distinction between the clearing house and the exchange itself. The clearing house does not get involved with physical delivery, nor does it provide any dispute settlement services. It only makes sure that cash is settled as and when due between the members. Therefore Choice 'c' is the correct answer

To calculate the Modified Duration from Macaulay's duration, we use the relationship MD = D/(1+r), where MD is the modified duration and D the Macaulay Duration. Therefore Choice 'c' is the correct answer.

A covered call is an attempt to earn premium income by selling calls while protecting against the downside by holding long the underlying. In case prices rise, the holder of the covered call can give away the held underlying. In case prices fall or stay below the strike price of the sold call, the holder of the covered call gets to keep the premium.

The holder of the covered call will suffer a loss if the price of the underlying declines due to the long position held in the underlying. However, these losses will be partly offset by the premiums earned on the calls sold.

Choice 'd' does not represent a correct statement as in the event of a rise in the price of the underlying the holder of the covered call will lose any upside, but will not have unlimited losses. In the event of a decline in stock prices, his losses will be equal to the loss on the underlying, minus the premium earned.

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.