Risk Budgeting
The revolution is risk management reflects the recognition that risk should be measured at the highest level, that is, firm wide or portfolio wide. This ability to measure total risk has led to a top-down allocation of risk, called risk budgeting. This concept is being implemented in pension plans as a follow-up to their asset allocation process. Asset allocation consists of finding the optimal allocation into major asset classes that provides the best risk return trade-off for the investor....
Credit Spread Risk
Credit spread risk is the risk that yields on duration-matched credit-sensitive bond and Treasury bonds could move differently. The topic of credit risk will be analyzed in more detail in the Credit Risk section of this book. Suffice to say that the credit spread represent a compensation for the loss due to default, plus perhaps a risk premium that reflects investor risk aversion. A position in a credit spread can be established by investing in credit-sensitive bonds, such as corporates,...
CrossRate Volatility
Exchange rates are expressed relative to a base currency, usually the dollar. The cross rate is the exchange rate between two currencies other than the reference currency. For instance, say that S1 represents the dollar pound rate and that S2 represents the dollar euro EUR rate. Then the euro pound rate is given by the ratio s3 eur bp ss 5 131 ln S3 ln Si - ln S2 13.2 of of of - 2p12a1 lt r2 13.3 Thus we could infer the correlation from the triplet of variances. Note that this assumes both the...
PriceYield Relationship 121 Valuation
The fundamental discounting relationship from Equation 1.1 can be extended to any bond with a fixed cash-flow pattern. We can write the present value of a bond P as the discounted value of future cash flows Ct the cash flow coupon or principal in period t t the number of periods e.g. half-years to each payment T the number of periods to final maturity y the discounting factor A typical cash-flow pattern consists of a regular coupon payment plus the repayment of the principal, or face value at...
Appendix Applications of Infinite Series
When bonds have fixed coupons, the bond valuation problem often can be interpreted in terms of combinations of infinite series. The most important infinite series result is for a sum of terms that increase at a geometric rate This can be proved, for instance, by multiplying both sides by 1 - a and canceling out terms. Equally important, consider a geometric series with a finite number of terms, say N. We can write this as the difference between two infinite series l a a2 a3 aN-l l a a2 a3 - aN...
Futures and Expected Spot Prices
An interesting issue is whether today's futures price gives the best forecast of the future spot price. If so, it satisfies the expectations hypothesis, which can be written as The reason this relationship may hold is as follows. Say that the 1-year oil futures price is F 20.47. If the market forecasts that oil prices in one year will be at 25, one could make a profit by going long a futures contract at the cheap futures price of F 20.47, waiting a year, then buying oil at 20.47, and reselling...
Tbond Futures
T-bond futures are futures contracts tied to a pool of Treasury bonds that consists of all bonds with a remaining maturity greater than 15 years and noncallable within 15 years . Similar contracts exist on shorter rates, including 2-, 5-, and 10-year Treasury notes. Treasury futures also exist in other markets, including Canada, the United Kingdom, Eurozone, and Japanese government bonds. Futures contracts are quoted like T-bonds, for example 97-02, in percent plus thirty-seconds, with a...
BlackScholes Valuation
We now briefly introduce the pricing of conventional European call and put options. Initially, we focus on valuation. We will discuss sensitivities to risk factors later, in Chapter 15 that deals with risk management. To illustrate the philosophy of option pricing methods, consider a call option on a stock whose price is represented by a binomial process. The initial price of S0 100 can only move up or down, to two values hence the bi , S1 150 or S2 50. The option is a call with K 100, and...
Answers to Chapter Examples
Example 1-1 FRM Exam 1999 Question 17 Quant. Analysis b This is derived from 1 yS 2 2 _ 1 y , or 1 0.08 2 2 _ 1.0816, which gives 8.16 . This makes sense because the annual rate must be higher due to the less frequent compounding. Example 1-2 FRM Exam 1998 Question 28 Quant. Analysis a This is derived from 1 yS 2 2 _ exp y , or 1 yS 2 2 _ 1.105, which gives 10.25 . This makes sense because the semiannual rate must be higher due to the less frequent compounding. Example 1-3 FRM Exam 1998...