Nellie Apostolova

Chapter 7 problem:

1. Valuing a forward contract

Example:
A woman wants to buy a house for $150,000 but she can't purchase it today. She enters into a forward contract with the owner who's selling the house for $142,000 and tells him that she will buy it in 1 year for 150,000. The risk free rate is .05. What is the forwarding price and who is going to wish they had not entered into the contract?

We'll use the formula for valuing a forward contract below:

(1)
\begin{equation} F_{o} = S_{o}(1+r^{f})^T \end{equation}

$F_{o}$ = What we're trying to find…
$S_{o}$ = Our current price which is $142,000
$r^{f}$ = risk free rate which is .05
$T$ = time which is 1 year

If we plug all that in and arrive at:

(2)
\begin{equation} F_{o} = 142,000(1+.05)^1 \end{equation}
(3)
\begin{equation} F_{o} = 149100 \end{equation}

In this case, the woman who's buying the house will wish he had not entered into the forward contract because she could have paid less than $150,000 for the house. She wouldn't be too upset because it's really only $900 less but it's still less. The seller of the house is happy that he entered into the forward contract because the contract price turned out to be higher.

Chapter 12 problem:

1. Price/earning ratio:

After a merger between two separate companies, Harper and Wyckoff, the price/earnings ratio of the merged firm is 22. If Harper accounts for 30% of the earnings and its price/earnings ratio is 14, what is Wyckoff's price/earnings ratio?

(4)
\begin{equation} P/NI = w_{H} (P_{H}/NI_{H}) + w_{W} (P_{W}/NI_{W}) \end{equation}

$P_{W}/NI_{W}$ = Price/earnings ratio of Wyckoff that we're looking for
$P/NI$= Merged price/earnings ratio equal to 22
$P_{H}/NI_{H}$= Price earnings ratio of Harper = 14
$w_{H}$= Percent of earnings contributed by Harper = 30% = .3
$w_{W}$= Percent of earnings contributed by Wyckoff = 1 -$w_{H}$= 70% = .7

22 = .7 ($P_{W}/NI_{W}$) + .3(14)
22 - .3(14) = .7 ($P_{W}/NI_{W}$)
17.8/.7 = 25.4 = 25 = $P_{W}/NI_{W}$

Chapter 21 problem:

1. Finding real exchange rate:

If in 2009, Britain's spot exchange rate is 1.45 pounds per US dollar. The local CPI is 3.0. The US CPI is 211.143. What is the real exchange rate?

(Spot Exchange Rate/local CPI)x US CPI = Real exchange rate
(1.45/3)x211.143 = 102.05 pounds per US dollar

Chapter 22 problems:

1. Assuming no arbitrage, what is the convenience yield that will produce a futures and forward price for a barrel of crude oil a year from now equal to $30.76. Current price is $17 a barrel and the risk free rate is 12%.

(5)
\begin{equation} F_{o} = S (1+r_{f}) / (1+y) \end{equation}

$F_{o}$ = $18.76
$S$ = $17.00
$r_{f}$ = .12
$y$ = what we're looking for

To solve:

$18.76 = 17 (1+.12) / (1+y)$
$18.76 = 19.04 / (1+y)$
$18.76 (1+y) = 19.04$
$1+y = 19.04/18.76$
$1+y = 1.0149$
$y = 1.0149 - 1$= .0149 or 1.49%

2. If John has an obligation to deliver 15 bushels of corn a year from now at a fixed price of $100 a bushel. European option to buy corn a year from now is $200 a bushel and has a forward delta of .15. How many of these options should John buy to eliminate price risk?

(6)
\begin{align} _{b} / \\delta \end{align}

$15/.15$ = 100

Chapter 23 problems:

1. If a 10 year bond has a DV01 of $.02 per $50 of face value and $15 million is purchased, what is its DV01 to perfectly hedge the interest rate risk of the portfolio?

$0 = -DV01_p + ((DV01 x $ of bond purchased)/(face value))$
$0 = -DV01_p + ((.02 * 15000000)/(50))$
$DV01_p = -6000$