35000: 85 InvestmentsHomework #2 January 31, 2015

We pledge our honor that we have not violated the Honor Code during the preparation of this assignment.

Jingyuan Huang Joon-Woo SongDaniel RaetchiRick Yeh

1If interest rate increases, yields fall. If interest rates decrease, yields rise. Convexity measures rate of change of price / yield curve. Bonds with greater convexity gain more in price when yields fall than they lose when yields rise.a. FALSE. Since A is more convex, it will fall less. b. TRUE.c. TRUE. A is more convex.d. FALSEe. FALSE

2a Present Value: Value today of some future amount.

2b With current investment we bought

Price of a Bond:

9% yield:

11% yield:

Future value is a function of the yield payable over the time we hold the asset. If the yield falls, it means our money will earn less over time, thus resulting in a lower future value. If the yield rises, it means our investment will earn mre over time, thus resulting in a higher future value.

2(c) i. Duration of Bond A

Duration of Bond B

x: invest in Bond A; x-1: invest in Bond B

PV of $1,000,000 liability:

2(c) ii.BOND ABond B

YieldPrice(from 2b)YieldPrice(same calc as in 2b)

9%$123.338 9%$138.506

11%$114.78411%$123.557

YieldLiabilityFV Bond A FV Bond B Total

P(r)1,000,000

9%1,000,000$555,629.49$455,192.53$1,000,347.11

11%1,000,000$545,154.58$444,709.31$1,000,338.80

By immunizing the portfolio in this way, we have actually made a little over $300 if the yield goes up or down by 1%.

2(c) iii. Bond Price after 1 year

Duration of Bond A

Duration of Bond B

x: invest in Bond A; x -1: invest in Bond B

Market Value of Investment: Bond Price + Coupon

NOTE: PV of $1,000,000 = $1,000,000 / (1.09)4 = $708,425.21 This is very close to the market value we have to invest.

WHAT HAPPENS IF YIELD MOVES 1% , to 8% or 10%?Price of BOND A (yr 1)Price of Bond B (yr 1)

YieldPriceYieldPrice

8%$123.1858%$143.728

10%$115.84910%$128.795

Comparisons of FV of Portfolio at 8%, 9% or 10% yield.YieldLiabilityFV Bond AFV Bond BTotal

P(r)1,000,000

8%1,000,000$741,498.88$259,823.72$1,001,322.60

9%1,000,000$745,944.52$255,031.56$1,000,976.08

10%1,000,000$750,450.93$250,560.09$1,001,011.02