# 文章详情

### FRM 2006-Market risk

Yesterday we posted the Section V Study Notes (Investments), a question set on Investments, and a new movie tutorial, Introduction to Value at Risk(VAR). We hope you agree this is the best way to learn about VAR. Thisweek’s movie is introductory: We review one-period VAR, absolute versusrelative VAR, and n-period VAR.
Interest rate parity (IRP) Theinterest rate parity (IRP) formula is a just a flavor of thecost-of-carry model that we reviewed in the last two posts. Thecost-of-carry model says the forward rate is a function of thecompounded spot rate. The difference is that, instead of an underlyingphysical commodity (e.g., corn, oil futures), we are dealing withforeign currency. So the forward exchange rate is a function of the spot exchange rate:

Inthe IRP, the spot exchange rate is simply the result of (continuously)compounding the difference between the domestic riskless rate and theforeign country riskless rate (r - rf). What if they happened to beequal? Then exp(0) = 1 and the forward exchange rate would equal thespot exchange rate. Why? Because if the country rates are equal, you’llend up at the same place regardless of whether you hold home currencyor covert immediately to foreign currency. The IRP, as a flavor of thecost-of-carry model, depends on the “no arbitrage” assumption: you needto be roughly indifferent to holding domestic or foreign currency.
Nowassume a 1.2 spot exchange rate, a domestic riskless rate of 5% and aforeign riskless rate is 2.75%. For a three month period (t=0.25), theIRP says the forward exchange rate must be 1.207:

Theforward rate must be higher. If it were not, you would always hold thedomestic currency and an arbitrage opportunity would (temporarily)exist.
Normal BackwardationKeep in mind that contango is not when the forward rate is greater than the spot rate. Contango is when the forward rate exceeds the expected spot rate:

Itis not obvious why the forward rate would be different from theexpected (future) spot rate. Contango is not what we expect; after all,why should we expect speculators to pay more for a futures contractthan its expected spot price. Normal backwardation, however, isreasonable when we consider that speculators (buyers of the foward contract) expect a profit.If speculators expect a profit, then they will pay something less thanthe expected (future) spot price. Therefore, normal backwardation is areasonable phenomenon: