Cashman Investments
Exam III In-Class Problems
1.
Put and call options are trading on Bilbo’s Bagging Company. Both options have an exercise price of $40 and one year to expiration. If the puts are selling for $2, and calls are selling for $8, what is Bilbo’s stock price? Assume that Bilbo’s does not pay dividends and that you can borrow and lend at 10%.
2.
Is it more valuable to own options on a portfolio of stocks, or a portfolio of options?
3.
What is the price of a two period put with an exercise price of $55? The stock currently sells for $45, the risk free rate is 10%, and each period the stock either increases or decreases $20.

4.
Next Friday the FDA will either approve DrugCo’s new miracle weight loss pill or reject the medication. If the FDA approves the medication we can expect DrugCo’s stock to go up $45, if it rejects the medication the stock will drop $45. Create a portfolio of options that will generate the largest profit regardless of the FDA’s decision? DrugCo’s stock is currently trading at $70, at the money puts and calls are selling for $10, puts and calls that are $15 out of the money are selling for $8. What is the portfolio of options you would create (You can only purchase 1 of each of the available options)? Draw out the payoffs of this strategy. How much will this portfolio make if the FDA approves the drug? How much does the portfolio make if the FDA rejects the drug?
5.
A corporate bond with a face value of $1,000 matures in 4 years and has a 8% coupon rate. The current price of the bond is $932. What is the yield to maturity for this bond?
6.
The MerryWeather Firm wants to raise $10 million to expand its business. It plans to sell 30-year, $1,000 face value zero-coupon bonds. The bonds will be priced to yield
7.
A 20 year 15% coupon bond has a YTC of 10.34%. If the bond is callable in 7 years at 115% of par what is its current price?
6%. What is the minimum number of bonds it must sell?

8.
What is the duration of a 3 year 12% coupon bond, if the YTM is 8%? How should the price of this bond be affected by a 75bp increase in interest rates?
9.
A 10% coupon bond has a YTM of 12%. If the bond’s duration is 23.7 and convexity is 276.4, what do you expect to be the effect of a drop in interest rates of 1.2%?

 Shares of Frodo’s Nasty Hobbit’s Co., currently trade at $135. How much will it cost you to purchase a call with an exercise price of $140 and that expires in a year? Puts with an exercise price of $140 are selling for $2, and the risk free rate is 25%.
Put call parity: C = S+P – PV(X)
C = 135 + 2 – (140/1.25)
= 137 – 112
=$25

Bob wants to buy a put option with a strike price of $40 on Matador Inc., a nondividend paying stock. The current stock price is $30, and Bob believe that the price will either increase to $60 or drop to $15 in 6 months. If the EAR is 21% per annum. How much would the put option cost Bob?
S t
S
T
P
1
$30
Spreads
$60
$15
$45=60-15
$0
$25
$25 =25-0
Delta = (25 / 45) = 5/9
Therefore, we need to short 5/9 of a share of Matador Inc
Since Matador stock is currently trading at $30 per share, this will generate
$16.67 = (5/9)*(30)
In the up state of the word the put is worth $0, but we need to spend -$33.33 (=
5/9 * 60) to close out our short position. Therefore we need a cash inflow to offset the cash outflow.
We lend the present value of $33.33
What is the rate we lend at for six months?
EAR = (1 + SAR/m) m - 1
0.21 = (1 + SAR/2) 2 - 1
SAR = 20%
The six month rate is 10%, so we lend $30.30 = 33.33/1.1
Shorting 5/9 of a share and lending $30.30 results in an out of pocket expense of
Cost is then $13.63 = 30.30-16.66


A corporate bond with a face value of $1,000 matures in 4 years and has an 8% coupon paid at the end of each year. The current price of the bond is $901. What is the yield to maturity for this bond?
N = 4, I/Y = ?, PV = -901, PMT = 80, FV = 1,000→ I/Y = 11.2%

If its yield to maturity is less than its coupon rate, a bond will sell at a _____, and increases in market interest rates will _____. premium; decrease this premium

The Lo Sun Corporation offers a 6% bond with a current market price of $875.05. The yield to maturity is 7.34%. The face value is $1,000. How many years is it until this bond matures?
N = ?, I/Y = 3.67, PV = -875.05, PMT = 30, FV = 1,000→ I/Y = 32
However, this is 32 semi-annual periods so the answer is 16 YEARS

Jackson Central has a 6-year, 8% annual coupon bond with a $1,000 par value. Earls
Enterprises has a 12-year, 8% annual coupon bond with a $1,000 par value. Both bonds currently have a yield to maturity of 6%. Which of the following statements are correct if the market yield increases to 7%? a. Both bonds would decrease in value by 4.61%. b. The Earls bond will increase in value by $88.25. c. The Jackson bond will increase in value by 4.61%. d. The Earls bond will decrease in value by 7.56%. e. The Earls bond will decrease in value by $50.68.

A 20 year 15% coupon bond offers an YTM of 12%. The bond is callable in 8 years at 113% of face value. What is the yield to call?
N = 40, I/Y = 6, PV= ?, PMT = 75, FV = 1,000 → PV = $1,225.69
N = 16, I/Y = ?, PV= -1225.69, PMT = 75, FV = 1,130 → I/Y = 5.81% Semi
Annual is 11.62%

You must pay out $1,256; $2,568; 5,896; and $1,867 respectively over the next 4 years.
What is the duration of this liability if the discount rate is 7%?
T (Semi)
1
CF
1,256
PV
1,207.69
Weight
0.116
W*t
0.116
2
3
4
Sum
2,568
5,896
1,867
2,374.26
5,241.52
1,595.92
10,419.39
0.228
0.503
0.153
1.000
0.456
1.509
0.613
2.693
Duration = 2.693 Years


The liabilities of your insurance company have a duration of 26 years. The only assets available to you to immunize your liabilities are 2 year zero coupon bonds and a 3% perpetuity. What percentage of your portfolio must you allocate to the perpetuity to immunize your portfolio?
Perp Duration = 1.03/0.03 = 34.333333
Zero Duration = 2
26 = wp * 34.3333 + (1-wp)*2
26 = 32.3333wp +2
24 =32.3333wp wp = 75.23%

What do you expect the price of a 12 years 9% (annual) coupon bond selling at par to be if the interest rate rises 50bp? The bonds duration is 41.3 and its convexity is 132.7.
ΔP/P = -D*(ΔY) + ½ * [Convexity * (ΔY) 2 ]
D* = 41.3/(1.12) = 36.875
ΔP/P = -36.875*(0.005) + ½ * [132.7 * (0.005) 2 ]
ΔP/P = -0.18438 + 0.001659 = -18.272%