# FNCE 4820 Fall 2013 Midterm 1 with Answers

David M. Gross, Ph.D.

Midterm 1 with Answers

Answer the questions in the space below. Written answer requires no more than a few sentences.

Show your work to receive partial credit. Points are as indicated.

1. (9 Points) Briefly define the following in the context of holding a bond.

(a) Interest-Rate Risk

Risk of price change due to changes in the bond’s yield.

(b) Inflation Risk

Risk of earning a lower-than-expected real return if inflation exceeds expectations.

(c) Liquidity Risk

The risk of a large price drop if the bond must be sold quickly or the inability to sell quickly without incurring a large price drop.

Note: Liquidity Risk can also refer to the inability of a

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(f) Use your calculations from parts (a) and (b) to compute the approximate Convexity (CX) for the bond.

CX ≈ (P- + P+ – 2P0)/(P0 x Δy2) = (1,111.04 + 904.61 – 2 x 1,000)/(1,000 x 0.012) = 156.50

(g) Use the bond’s modified duration calculated in part (c) AND the convexity calculated in part (f) to estimate the dollar change in price of the bond for a 100 bps increase in yield.

ΔP ≈ (-D* x P00 x Δy) + (½CX x P00 x Δy2) = (-10.32 x 1,000 x 0.01) + [½(156.50) x 1,0000 x (0.01)2] = -103.22 + 7.82 = -95.39

(h) Compare your estimations from parts (e) and (g) to the actual change computed in part (d). Briefly explain why your estimation from part (g) is better than your estimation from part (e).

The estimation using both Duration and Convexity from part (g) is better since it corrects for the “curvature” or “change in slope” of the price/yield relationship.

See Exhibit 4-13 on page 75 of the text.

8. (6 Points) A $100 million bond portfolio has the following three bonds.

Bond

Market Value

D*

A

$25,000,000

5

B

$25,000,000

7

C

$50,000,000

2

(a) Estimate the PVPB (also called the DV01) for the portfolio.

Port D*= ∑ w x D* = 0.25(5) + 0.25(7) + 0.5(2) = 4

PVBP = ΔP ≈ (-D* x P00 x Δy) = D* x P x 0.0001 = 4 x $100,000,000 x 0.0001 = $40,000

(b) Assume the portfolio