# Portfolio duration

Can someone help me understand this question a little better from Schweser?

Donald McKay, CFA, is analyzing a client’s fixed income portfolio. As of the end of the last quarter, the portfolio had a market value of \$7,545,000 and a portfolio duration of 6.24. McKay is predicting that the yield for all of the securities in the portfolio will decline by 25 basis points next quarter. If McKay’s prediction is accurate, the market value of the portfolio:

Can someone point me to a formula for this question? I understand a little bit after reading the explanation, but I feel like the readings aren’t helping me really understand.

Change in Price = -1 * DeltaR * Duration

= -1 * - 0.0025 * 6.24 = + 0.0156

So MV of Portfolio = 7,545,000 * (1+0.0156) = \$ 7,662,702

Thanks!

Is this only applicable under certain circumstances that would be discernable in the question? Like all of the bonds move in the same direction and move by the same amount? or there are no embedded options?

If they are not talking about any embedded options you can safely assume there are none. Also you are given a portfolio duration, so you do not need to worry what the individual bonds are doing (in this particular question).

Higher duration bonds are more sensitive to interest rate changes. As interest rates rise, your bond prices will fall. %∆P = -MD*∆Y. As interest rates fall, bond prices rise.

Bonds with higher convexity will fall less as interest rates rise, and gain more as rates lower. ∆%P = -MD*∆Y + 1/2C∆Y^2. Convexity is a second derivative effect that helps improve estimates of price change.