Revision as of 17:01, 20 November 2023 by Admin (Created page with "'''Solution: D''' The price of Bond <math>\mathrm{A}</math> is <math>60\left(1.04^{-1}+1.04^{-2}+1.04^{-3}\right)+1000\left(1.04^{-3}\right)=1055.50</math>, while the Macaulay duration of Bond A is <math display = "block">\frac{60\left[1.04^{-1}+2\left(1.04^{-2}\right)+3\left(1.04^{-3}\right)\right]+3(1000)\left(1.04^{-3}\right)}{1055.50}=2.838</math>. Note that the one-year zero-coupon bond has duration 1. Let <math>w</math> denote the proportion of wealth to invest...")
Exercise
Nov 20'23
Answer
Solution: D
The price of Bond [math]\mathrm{A}[/math] is [math]60\left(1.04^{-1}+1.04^{-2}+1.04^{-3}\right)+1000\left(1.04^{-3}\right)=1055.50[/math], while the Macaulay duration of Bond A is
[[math]]\frac{60\left[1.04^{-1}+2\left(1.04^{-2}\right)+3\left(1.04^{-3}\right)\right]+3(1000)\left(1.04^{-3}\right)}{1055.50}=2.838[[/math]]
. Note that the one-year zero-coupon bond has duration 1.
Let [math]w[/math] denote the proportion of wealth to invest in Bond A; then, [math]1-w[/math] is the proportion of wealth invested in Bond B. Then [math]2=2.838 w+1(1-w)[/math], or [math]w=0.5440[/math].
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.