A portfolio comprises 2-year, 5-year, and 10-year zero-coupon bonds with $100 value in each position. Factor...

Transcribed Image Text:

A portfolio comprises 2-year, 5-year, and 10-year zero-coupon bonds with $100 value in each position. Factor movements affecting key rates of the yield curve are as follows. Year Parallel 2 5 10 1 1 1 Steepness -1 0 1 Curvature 1 -1/2 1 For a parallel factor increase of 1%, year 2 bond yield increases by 1%, year 5 bond yield increases by 1%, and year 10 bond yield increases by 1%. For a steepness factor increase of 1%, Year bond yield decreases by 1% and year 10 bond yield increases by 1%. For a curvature factor increase of 1% (yield curve becoming less convex), Year 1 bond yield increases by 1%, Year 2 bond yiel decreases by 12% and year 10 bond yield increases by 1%. (a) What is the key rate duration of the portfolio to the two-year rate, 5-year rate, and 10-year rate? (Assume current 2, 5, 10 year yields are very small, 1 to 2 %). (b) If AX, AY, AZ denote % changes in the parallel, steepness, and curvature factors, and we define AP/P = - A1 AX-A2 AY - A3 AZ where P is current value of portfolio, P= $300, then find the values of A1, A2, and A3. (c) Suppose there is a steepening of the yield curve the next moment and only the steepness factor increases by ½ %, what is the change in the dollar value of the portfolio? A portfolio comprises 2-year, 5-year, and 10-year zero-coupon bonds with $100 value in each position. Factor movements affecting key rates of the yield curve are as follows. Year Parallel 2 5 10 1 1 1 Steepness -1 0 1 Curvature 1 -1/2 1 For a parallel factor increase of 1%, year 2 bond yield increases by 1%, year 5 bond yield increases by 1%, and year 10 bond yield increases by 1%. For a steepness factor increase of 1%, Year bond yield decreases by 1% and year 10 bond yield increases by 1%. For a curvature factor increase of 1% (yield curve becoming less convex), Year 1 bond yield increases by 1%, Year 2 bond yiel decreases by 12% and year 10 bond yield increases by 1%. (a) What is the key rate duration of the portfolio to the two-year rate, 5-year rate, and 10-year rate? (Assume current 2, 5, 10 year yields are very small, 1 to 2 %). (b) If AX, AY, AZ denote % changes in the parallel, steepness, and curvature factors, and we define AP/P = - A1 AX-A2 AY - A3 AZ where P is current value of portfolio, P= $300, then find the values of A1, A2, and A3. (c) Suppose there is a steepening of the yield curve the next moment and only the steepness factor increases by ½ %, what is the change in the dollar value of the portfolio?

Answer rating: 100% (QA)

To answer question a regarding the key rate duration of the portfolio to the twoyear rate fiveyear rate and tenyear rate we would generally need to calculate how the value of each bond in the portfoli... View the full answer