开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

小熊猫 · 2023年11月08日

duration计算

NO.PZ2023091802000081

问题如下:

A portfolio manager is analyzing the impact of yield changes on two portfolios: portfolio ASD and portfolio BTE. Portfolio ASD has two zero-coupon bonds and portfolio BTE has only one zero-coupon bond. Additional information on the portfolio is provided in the table below:

To assess the potential effect of a parallel shift in the yield curve on portfolio values, the manager runs a scenario in which yields increase by 200 bps across all points of the yield curve. In addition, the manager estimates a convexity of 34.51 for portfolio ASD and 36.00 for portfolio BTE. Assuming continuous compounding, which of the following are the best estimates of the decrease in the values of the two portfolios due to the combined effects of duration and convexity?

选项:

Portfolio ASD Portfolio BTE

A.

USD 102,000 USD 65,000

B.

USD 110,000 USD 70,000

C.

USD 118,000 USD 74,000

D.

USD 127,000 USD 79,000

解释:

Step 1 - Calculate the values of the two portfolios before increases in yield:

Portfolio ASD

PA = Value before yield increase: 1,000,000*exp(-0.1*3) + 1,000,000*exp(-0.1*9)

= USD 740,818.22 + USD 406,569.66 = USD 1,147,387.88

Portfolio BTE

PB = Value before yield increase: 1,000,000*exp(-0.08*6) = 618,783.39

Step 2 - Calculate the duration of the two portfolios before increases in yield:

Portfolio ASD

DA = weighted-average durations of the two zero-coupon bonds

= DA*WA + DB*WB = 3*(740,818.22/1,147,387.88) + 9*(406,569.66/1,147,387.88) = 5.13

Portfolio BTE

DB = duration of portfolio BTE = 6.00 (duration is approximately same as maturity for a

zero-coupon bond).

Step 3 – Note the convexities given for the two portfolios (no need to calculate):

CA = 34.51; and CB = 36.00

Step 4 - Estimate the changes in portfolio values due to the yield change (y) and the

effects of duration and convexity:

Change in bond value = ΔP = -P*D*Δy + ½*P*C*(Δy)2

Portfolio ASD

ΔPA = -PA*DA*Δy + ½*PA*CA*(Δy)2

= -1,147,387.88*5.13*0.02 + 0.5*1,147,387.88*34.51*(0.02)2

= -117,722.00 + 7,919.27 = USD -109,802.73

Portfolio BTE

ΔPB = -PB*DB*Δy + ½*PB*CB*(Δy)2

= -618,783.39*6.00*0.02 + 0.5*618,783.39*36*(0.02)2

= -74,254.00 + 4,455.24 = USD -69,798.76

A is incorrect. The change in value for both portfolios are wrongly computed as the parameter 0.5 is left out in the convexity formula.

C is incorrect. The changes in value for both portfolios do not consider the effect of convexity.

D is incorrect. Changes in value for both portfolios are wrongly computed by inserting a negative sign (rather than a positive) in the convexity part of the formula.


题里给的是macaulay duration 计算中用的是effective duration?

不应该用mac d/(1+Y)来计算effective duration吗?怎么直接就用mac d了呢?

1 个答案

品职答疑小助手雍 · 2023年11月08日

同学你好,这题并没有说让用哪种duration进行计算,计算里只是说到了“combined effects of duration and convexity”,“结合久期和凸性的影响”。

一般零息债的题目直接用期限作为duration就可以了。

另外,你用mac d/(1+Y)算出来的应该是modified duration,而不是effective duration。

  • 1

    回答
  • 0

    关注
  • 336

    浏览
相关问题