Hi
@ann123456 Yes you are correct that bond price returns VaR is the product of a
change in yield and
modified duration! However,
Yield VaR is a change in yield. Let's take Jorion's own example, see below, for the 7-year term. The yield VaR is 0.484%. I don't think he anywere decomposes the yield VaR but Yield VaR = (Yield volatility) * (deviate); e.g., if yields are normal, then if the yield volatility is 1.0%, then the 95.0% yield VaR = 1.0% * 1.645 = 1.645%. So probably his 7-year yield VaR of 0.484% = 0.294% yield volatility * 1.645 = 0.484%. This is just a way of scaling volatility: "if the yield volatility is 294 basis points, then our worst expected change with 95% confidence is 484 basis points." In this way, this is a measure of yield change. Therefore, 7-year returns var = yield VaR * modified duration = 0.484% * 7/(1+6.07%) = 3.192 because the 0.484% itself is Δy*z(α), so we have returns VaR = Δy*z(a)*[Mac_duration/(1+y)] = 0.294%*1.645*(7/1.067) = 3.173%. I hope that helps!
Stay connected