You are a Swedish investor owning a portfolio of Swedish and American stocks. Their
respective benchmarks are the OMX index and the S&P index. There have been no
movements during the year (cash flows, sales, or purchase). Dividends of SKr 20,000
have been paid on Swedish stocks. Valuation and performance analysis is done in
Swedish krona (SKr). Here are the valuations at the start and the end of the year:
a. What is the total value of the portfolio in SKr on January 1 and on December 31?
b. What is the total return on the portfolio?
c. Decompose this return into capital gain, yield, and currency contribution.
d. What is the contribution of security selection?
A small French bank has the following balance sheet, based on historical (nominal)
values.
All assets and liabilities are denominated in euros. The net worth is calculated as the
difference between the value of assets and liabilities. The current interest rate term
structure in euro is flat at 8%. The risk premium over Euribor required on the loan to a
client remains at 50 basis points.
a. Value the balance sheet based on market value.
b. The bank anticipates a sharp drop in French interest rates. Would this drop be good
for the bank?
The current market conditions for interest rate swaps with a maturity of three or five
years are 8% against Euribor.
c. Assume that the bank simply wishes to immunize its market value against any
movements in interest rates (drop or rise). What swap would you make to hedge this
interest rate risk?
d. Assume that the bank is quite confident in its interest rate prediction (a drop). What
would you suggest?
The next day, all interest rates drop to 7%.
e. Value the balance sheet again, assuming that the floating rate debt remains at 100%
and that the bank has undertaken the swap that you recommended. How much did the
bank save by undertaking this swap?
A zero-coupon bond with a five-year maturity is worth 68.06% of its final
reimbursement value.
a. Verify that its actuarial yield-to-maturity is equal to 8% by compounding 8% over
five years.
b. What is the simple yield of this bond, and why is it so different from the actuarial
yield?
An American investor holds a British bond portfolio worth 100 million. The portfolio
has a duration of 7. She fears a temporary depreciation of the pound but wishes to retain
the bonds. To cover this risk, she decides to sell pounds forward. She has observed that
the British government tends to adopt a “leaning-against-the-wind” policy. When the
pound depreciates, British interest rates tend to rise to defend the currency. A regression
of “variations in long-term British yields” on “percentage exchange rate
movements” has a slope coefficient of -0.1. In other words, British yields tend to
go up by 10 basis points (0.1%) when the pound depreciates by 1% relative to the
dollar.
a. What should be the optimal hedge ratio used by the investor if she wishes to reduce
the uncertainty caused by exchange risk? (The investor uses only forward currency
contracts to hedge this risk, not bond futures contracts.)
b. Detail the factors that could make this hedge imperfect if the depreciation of the
pound materializes.
Fundamental Value Based on Absolute PPP. Ideally, one would like to compare
directly the price
of goods in two countries to see if an exchange rate conforms to absolute PPP, or
whether it is overvalued or undervalued in real terms. As mentioned in Chapter 2, this
can only be done for some individual goods that are clearly comparable (“law of one
price”), and the estimation for different goods can lead to opposing conclusions. In
Chapter 2, we provide an analysis based on the well-known Big Mac report of The
Economist. Of course, the Big Mac is a very particular product and a fundamental PPP
value can be computed on a wide range of products. The results are often conflicting.
For example, one can look at production prices rather than consumption prices. Some
studies are conducted by looking at labor costs. Rather than looking at unit labor costs
for unskilled workers, as is often done, the exhibit below reports the average annual
remuneration of the chief executive officer (CEO) of industrial companies with annual
revenues of 250 million to 500 million in ten selected areas of the world. The
figures are also from April 199 They include all forms of compensation, such as
bonuses, perks, and stock options, but are not adjusted for different taxes or costs of
living.
The first column gives the total CEO compensation measured in U.S. dollars using the
actual exchange rate, which is indicated in the second column. The third column gives
the fundamental PPP value of each currency, implied by the national CEO
compensations. It is the exchange rate with the dollar that would make CEO
compensation identical in all countries. The fourth column gives the actual
overvaluation (if positive) or undervaluation (if negative) of the local currency relative
to its fundamental value in terms of CEO compensation.
EXHIBIT: Determining a Fundamental PPP Value Based on CEOs€ Remuneration
Source:Total compensation data comes from Towers Perrin, 1998.
What conclusions can you draw from this exhibit?
A hedge fund currently has assets of $500 million. The annual fee structure of this fund
consists of a fixed fee of 1% of portfolio assets plus a 20% incentive fee. The fund
applies the incentive fee to the gross return each year in excess of the portfolio’s
previous high watermark, which is the maximum fund value in the past two years. The
fund is closed to new investors and the maximum value that the fund has achieved in
the past two years was $520 million. Compute the fee that the manager will earn, in
dollars, if the return on the fund in the coming year turns out to be:
a. 30%
b. 2%
c. -2%
A young investment banker considers issuing a DM/$ currency option bond for a AAA
client and wonders about its pricing. He knows that currency options are available on
the market and that they could help set the conditions on the bond issue. As a first step,
he decides to study a simple case: a one-year bond. The current market conditions are as
follows:
·One-year dollar interest rate: 10%.
·One-year Deutsche mark interest rate: 7%.
·Spot DM/$ exchange rate: $1 = DM 2.
The banker could issue a bond in dollars at 10%, a bond in DM at 7%, or a currency
option bond at an interest rate to be determined. One-year currency options are
negotiated on the over-the-counter market. A one-year currency option to exchange one
dollar for two Deutsche marks is quoted at 4%, that is, four cents per dollar. This is a
European option, which can be exercised only at maturity. The one-year forward
exchange rate is:
a. Given these data, what should the interest rate be on a one-year DM/$ bond?
b. How would you determine how to set the interest rate on an -year currency bond?
You invest in a country named Papaf. You observe the stock returns on a list of stocks
during
three periods.
You consider explaining differences in returns by common factors, with a linear model
as represented in Equation (6.9). You have two candidates for factors: movements in
interest rates and changes in the local temperature measured at noon-time from the
previous day. The various values of these factors are given below:
a. Try to assess whether each factor has an influence on stock returns.
b. Try to estimate the intercept and the factor exposures of each asset.
Strumpf Ltd. decides to issue a convertible bond with a maturity of two years. Each
bond is issued with a nominal value of 100 and an annual coupon C; of course, C has to
be determined. Each bond can be redeemed for 100 or converted into one share of
Strumpf at the option of the bondholder.
The current stock price of Strumpf is 90. The yield curve for an issuer like Strumpf is
flat at 6%. Barings is ready to issue long-term options on Strumpf shares. The
premiums on calls with one-year and two-year expirations are given below:
a. American-type calls are more expensive than European-type calls. Is it reasonable?
b. Assume that the bond can only be converted at maturity, after payment of the second
coupon. What should be the fair coupon rate C, consistent with the above market
conditions?
c. Assume that the bond is issued with the coupon rate determined above. The yield
curve suddenly moves from 6% to 6.1% and the option premiums stay the same. What
should be the new market price of the convertible bond?
d. Assume now that the bond can be converted on two dates (rather than one as above).
These dates are the first year (right after the first coupon payment) and the second year
as above. It is not possible to convert the two-year bond at any other date. Is it possible
to construct an arbitrage portfolio allowing to price the fair coupon C with the above
data? Be precise in your explanation and state what type of options you would need to
price the bond.
A company without default risk can issue a perpetual FRN at LIBOR. The coupon is
paid and reset semiannually. It is certain that the issuer will never have default risk and
will always be able to borrow at LIBOR. The FRN is issued on November 1, 2005,
when the six-month LIBOR is at 4.5%. On May 1, 2006, the six-month LIBOR is at
5%.
a. What is the coupon paid on May 1, 2006, per $1,000 bond?
b. What is the new value of the coupon set on the bond?
c. On May 2, 2006, the six-month LIBOR has dropped to 4.9%. What is the new value
of the FRN?
Bank PAPOUF decides to issue two bonds and wonders what the fair interest rate on
these bonds should be:
A. A one-year currency option bond. The bond is issued in dollars with a face value of
$100. The bondholder can choose to have the coupon and principal paid in dollars or in
SFr, at a specified exchange rate of SFr/$ = 2, that is, receive either $100 or SFr 200 as
principal repayment, and receive either $C or SFr 2C as interest if C is the coupon set in
dollars. The coupon rate is
c = C/100.
B. A two-year currency option bond. The bond is issued in dollars, with a face value of
$100 and pays an annual coupon C¢. The bondholder can choose to have the coupons
and principal paid in dollars or in SFr, at a specified exchange rate of SFr/$ = 2, that is,
receive either $100 or SFr 200 as principal repayment, and receive either $C’ or SFr
2C’ as interest, if C’ is the coupon set in dollars. The coupon rate is c’ = C’/100.
Current market conditions are given below:
· Interest Rates 1-Year 2-Year
Zero-coupon rates
US$ 8% 8%
SFr 4% 4%
· Spot exchange rate: SFr/$ = 2
· Currency options:
SFr call, strike price 50 U.S. cents, expiration one year: 2 U.S. cents.
SFr call, strike price 50 U.S. cents, expiration two years: 5 U.S. cents.
a. Compute the coupon C on Bond A that would be consistent with market conditions at
time of issue.
b. Compute the coupon C‘ on Bond B that would be consistent with market conditions
at time of issue.
Survivorship bias is a serious potential problem in drawing conclusions from historical
track records. Show why the following statements can be misleading:
a. “There are today 100 Type-A hedge funds in operation. Their average return over the
past two years is 20%. Hence, they have outperformed the stock market (return of
15%)” [actually, some 50 funds disappeared during these two years].
b. “The Poupou commodity index has been back-calculated from 1970 to 1990 using
the leading commodity futures contracts; by leading we mean those that have been most
active. The Poupou commodity index had a remarkable performance from 1970 to
1995″ [actually, several commodity futures contracts have been removed from the
commodity exchange or have experienced a drop in trading activity].
Titi, a Japanese company, issued a six-year Eurobond in dollars convertible to shares of
the Japanese company. At time of issue, the long-term bond yield on straight dollar
bonds was 10% for such an issuer. Instead, Titi issued bonds at 8%. Each $1,000 par
bond is convertible into 100 shares of Titi. At time of issue, the stock price of Titi is
1,600 yen and the exchange rate is 100 yen = 0.5 dollar
($/Y = 0.005).
a. Why can the bond be issued with a yield of only 8%?
b. What would happen if:
·The stock price of Titi increases?
·The yen appreciates?
·The market interest rate of dollar bonds drops?
c. A year later, the new market conditions are as follows:
·The yield on straight dollar bonds of similar quality has risen from 10% to 11%.
·Titi stock price has moved up to Y 2000.
·The exchange rate is $/Y = 0.006.
·What would be a minimum price for the Titi convertible bond?
d. Could you try to assess the theoretical value of this convertible bond as a package of
other securities such as a straight bond issued by Titi, options or warrants on the yen
value of Titi stock, an futures and options on the dollar/yen exchange rate?
The investment fund of Lemon County of California is investing $1 billion in a
leveraged-bond hedge fund. This hedge fund has the following structure:
· $4 billion invested in a reverse-floater (also called bull FRN). This is a five-year bond
with a coupon set at: 9% minus three-month LIBOR.
· $3 billion borrowed at: three-month LIBOR.
The current yield curve is flat at 4.5%. The reverse floater is currently priced at 100%.
a. Estimate the yield-enhancement over LIBOR that the hedge fund would provide if
the yield curve drops uniformly by 10 basis points (0.1%).
Actually, the whole yield curved moved up to 7% within a few days.
b. What would be the new income (coupon rate) on this $1 billion investment made by
Lemon County?
c. Can you provide some rough estimate of the new market value of this $1 billion
investment?
Assume that the domestic volatility (standard deviation in yen) of the Japanese stock
market is 18%. The volatility of the yen against the U.S. dollar is 6%.
a. What would the dollar volatility of the Japanese stock market be for a U.S. investor if
the correlation between the Japanese stock market returns and exchange rate
movements were zero?
b. Suppose the dollar volatility of the Japanese stock market is 18.4%, what can you
conclude about the correlation between the Japanese stock market movements and
exchange rate movements?
Your pension fund decides to invest in many national stock markets in a passive way.
The objective is to try to match the performance of the local market
capitalization-weighted index in each country. You do not buy national index funds but
invest directly in companies listed on each market. Because of the limited size of your
portfolios, you can buy only a few issues in each market. In which national markets are
you likely to track the index well or poorly?
The euro was introduced in 1999 as the common currency of eleven European countries
(Euroland). What should happen to the inflation rates of France, Germany, and Italy
after the introduction of the common currency?
You are a money manager of French stocks. Your research department prepared the
table below. According to the domestic CAPM for French securities, which stocks
would you recommend for purchase and sale?
An Italian importer will be paid $1 million in three months (March). He must decide
whether to sell $1 million forward or to buy currency options for that amount.
The current market prices are as follows:
Exchange rates: Spot = 1.10
Three-month forward: = 1.11
Call euro March 110 U.S. cents: 1.5 U.S. cents per .
Put euro March 110 U.S. cents: 1.0 U.S. cents per .
What are the differences between the strategies of selling currency forward and buying
currency options?
The bid-ask rates are as follows:
Spot exchange rate:
CHF/USD: 1.5500-1.5540
Interest rates:
One-month CHF 31/2 – 5/8
One-year CHF 41/4 – 1/2
One-month USD 61/8 – 1/4
One-year USD 61/2 – 3/4
What are the quotations for the one-month and one-year CHF/USD forward exchange
rates?