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International Investment Management End term summary
Summary for the course ECB3BL International investment management (end term and mid term summary)
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Olivier van den Wall Bake - 5510929International Investment Management Summary (ENDTERM)
Chapter 15, Term Structure of Interest Rates
The yield curve
o Is a graph that displays the relationship between yield and maturity
o Information on expected future short term rates can be implied from the yield curve
An upward sloping yield curve is evidence that short-term rates are going to be higher next year
When next year’s short rate is greater than this year’s short rate, the average of the two rates is higher than today’s rate
Expectations theory
o Observed long-term rate is a function of today’s short-term rate and expected future short-term rates
Long term and short term securities are perfect substitutes
Forward rates that are calculated from the yield on long-term securities are market consensus expected future
short term rates
Long term bonds are more risky
o Investors will demand a premium for the risk associated with long-term bonds
o The yield curve has an upward bias built into the long-term rates because of the risk premium
Forward rates contain a liquidity premium and are not equal to expected future short-term rates
Spot rate
o The YTM on a zero coupon bond
Forward interest rate
o Is the rate that is inferred from the growth of the observed interest rates of the years before
In general, to construct the synthetic forward loan, you sell (1+f 2) 2-year zeros for every 1-year zero that you buy. This makes your initial
cash flow zero because the prices of the 1-and 2-year zeros differ by the factor (1+f 2)
Forward rates are market interest rates in the important sense that commitments to forward borrowing or lending arrangements can
be made at these rates.
Economic forecasts as explanation of yield curve
o Expansion rise
o Contraction inverted yield curve
Forward rates will generally not equal realized short rates
Forward rates can be used to agree today on a loan which commences at a future date
See calculation about how to create a forward loan
Chapter summary
The term structure of interest rates refers to the interest rates for various terms to maturity embodied in the prices of default free zero
coupon bonds
In a world of certainty all investments must provide equal total returns for any investment period. Short term holding period returns on
all bonds would be equal in a risk free economy and all equal to the rate available on short term bonds. Similarly, total returns from
rolling over short term bonds over longer periods would equal the total return available from long maturity bonds
The forward rate of interest is the break even future interest rate that would equate the total return from a rollover strategy to that of a
longer term zero coupon bond.
A common version of the expectations hypothesis holds that forward interest rates are unbiased estimates of expected future interest
rates. However, there are good reasons to believe that forward rates differ from expected short rates because of a risk premium known
as a liquidity premium. A positive liquidity premium can cause the yield curve to slope upward even if no increase in short rates is
anticipated.
The existence of liquidity premiums makes it extremely difficult to infer expected future interest rates from the yield curve. Such an
inference would be made easier if we could assume the liquidity premiums remained reasonably stable over time. However ,both
empirical and theoretical considerations cast doubt on the constancy of that premium
,Olivier van den Wall Bake - 5510929
Chapter 16.1, managing bond portfolios
Bond pricing relationships
1. Bond prices and yields are inversely related
1. Bond prices decrease when yields rise
2. Price curve is convex
3. Decreases in yields have bigger impacts on price than
increases in yields of equal magnitude
2. An increase in a bond’s YTM results in a smaller price change than a decrease in
yield of equal magnitude
3. Prices of long-term bonds tend to be more sensitive to interest rate changes than
prices of short-term bonds
4. The sensitivity of bond prices to changes in yields increases at a decreasing rate as
maturity increases. In other words, interest rate risk is less than proportional to bond maturity
i. As maturity increases, price sensitivity increases at a decreasing rate
5. Interest rate risk is inversely related to the bond’s coupon rate. Prices of low-coupon bonds are more sensitive to changes
in interest rates than prices of high-coupon bonds
i. Price sensitivity is inversely related to a bond’s coupon rate
6. The sensitivity of a bond’s price to a change in its yield is inversely related to the YTM at which the bond is currently
selling
Maturity is a major determinant of interest rate risk
The effective maturity of a bond is therefore some sort of average of the maturities of all the cash flows.
Price sensitivity tends to increase with the time to maturity
Macaulay’s durations
o Equals the weighted average of the times to each coupon or principal payment.
CF t
(1+ y)t
w t=
Bond price
o A measure used to calculate the value of a fixed income security that will result from a 1% change in interest rates
Duration is shorter than maturity for all bonds except zero coupon bonds
Duration is equal to maturity for zero coupon bonds
Duration is a key concept in fixed-income portfolio management for at least three reasons
o It is a simple summary statistic of the effective average maturity of the portfolio
o It turns out to be an essential tool in immunizing portfolios from interest rate risk
o Duration is a measure of interest rate sensitivity of a portfolio
The proportional change in a bond’s price can be related to the change in its yield to maturity, y
∆P ∆ ( 1+ y )
o =−D∗[ ]
P 1+ y
o The proportional price change equals the proportional change in 1 plus the bond’s yield times the bond’s duration
Modified duration
D
o D¿ = with ∆ (1+ y )=∆ y
(1+ y )
∆P
o To =−D∗∆ y
P
o The percentage change in bond price is just the product of modified duration and the change in the bond’s yield to
maturity
Price change is proportional to duration and not to maturity!!!!!
Because the percentage change in the bond price is proportional to modified duration, modified duration is a natural measure
of the bond’s exposure to changes in interest rates
The modified duration formula is only approximately valid for large changes in the bond’s yield. The approximation becomes
exact as one considers smaller, or localized, changes in yields.
Duration is shorter than maturity for all bonds except zero coupon bonds
o Duration is equal to maturity for zero coupon bonds
Macaulay’s duration
o A measure of the effective maturity of a bond
The weighted average of the times until each payment is received. With the weights proportional to the
present value of the payment
o A measure used to calculate the value of a fixed income security that will result from a 1% change in interest rates
Duration is shorter than maturity for all bonds except zero coupon bonds
Duration is equal to maturity for zero
Chapter summary
,Olivier van den Wall Bake - 5510929
Even default-free bonds such as treasury issues are subject to interest rate risk. Longer-term bonds generally are more sensitive to interest
rate shifts than are short-term bonds. A measure of the average life of a bond is Maucalay’s duration, defined as the weighted average of
the times until each payment made by the security, with weights proportional to the present value of the payment.
Chapter 20 Option markets Introduction
Investment management
o Managing assets in such a way that expected return and risk are balanced
Options are derivative securities, or contingent claims because the payoff depends on the prices of other securities. Options
have two varieties
o Call options
o Put options
Call option
o Gives its holder the right to purchase an asset for a specified price, called the exercise price, or strike price.
o The purchase for the specific price has to be made on a specified expiration date, or before that date. Sellers of
these call options are said to write calls, who receive a premium as their income.
The purchase price of the option is called the premium
o It represents the compensation the purchaser of the call must pay for the right to exercise the option only when
exercise is desirable
The holder of the call option will only use his right to buy the asset if the market price is higher than the strike price he has to
pay for it. This difference is called the value of the option.
The net profit of a call option is the value of the option minus the original price paid to purchase it.
Put option
o Gives its holder the right to sell an asset for a specified price on or before the expiration date.
o Opposite to call option, profits of put options increase when the value of the asset falls. The owner of a put option
only exercises this option if the market price of shares is lower than the strike price of the option. The difference
between the two is his profit.
An option is called in the money when it delivers profits and out of the money when it does not. If the market price of the
assets equals the exercise price the option is called to be at the money
Options can be traded on over-the-counter markets and on exchanges. On exchanges options are standardized which highly
facilitates the trading process because all participants trade in a limited and uniform set of securities.
o Two benefits
Trading becomes easier
A liquid secondary market of options
All exchanges trading in options jointly own the Operations Clearing Corporation (OCC)
o Clearinghouse for options trading
o The OCC is the effective buyer and seller of options and thus functions as the intermediate.
Option contract terms can be adjusted if the security is changed.
o EX
Stock splits are passed on to the value of the option. A 2 for 1 split of a stock would also split one option
into two options both half the value of the former option
There is a difference between American and European options.
o American option (in reality on the exchanges)
Allows the holder of the option to exercise it on or before the expiration date
o European option
Only allows exercise on the expiration date itself
Options are also traded on other assets than stocks, such as indexes, foreign currency, gold or future prices of agricultural
products.
Value of the option at expiration
o The profit to the call option holder is the value of the option at expiration minus the original purchase price
Call options
o Payoff to call holder
ST −X if ST > X
0 if ST ≤ X
St is the value of the stock at expiration and X is the exercise price
profit to call holder: Payoff – purchase price
o Payoff to call writer
−( S T − X )if ST > X
0 if ST ≤ X
the call writer is willing to bear the risk to lose in return for the option
premium
,Olivier van den Wall Bake - 5510929
profit to call writer: Payoff + premium
Put options
o Payoff to put holder
0 if ST ≥ X
X −S T if ST < X
profit to put writer: Payoff + premium
Payoff to put writer
o
0 if ST ≥ X
−( X−ST ) if S T < X
Profit to put writer: Payoff + premium
Simply writing puts exposes the writer to losses if the market price of the stock falls. Writing puts out of the money was
considered a fairly safe investment as long as the market would not fall very sharply.
Bullish strategies
o Purchasing call options and writing put options
o Long and short position in calls, different exercise prices (bullish spread)
o Profits from over- or underpricing (bullish spread)
Bearish strategies
o Purchasing put options and writing call options
Two important reasons could be given to explain investor’s eagerness to buy options
o Options enable leverage
Their values respond more than proportionately to the stock value
o Options offer a potential insurance value
Option strategies
o Protective put
Combines investment in normal stock with the purchase of put options of the same stock.
The result is that whatever happens to the stock price, you are guaranteed a payoff at least equal to the
put option’s exercise price, because the put gives you the right to sell your shares for that price.
Form of portfolio insurance, protecting your shares against a decline, using a put option
Cost
o In case the stock price increases, your profit is reduced by the cost of the put,
which turned to be unneeded.
o Covered call
Purchase of a share of stock combined with the sale of a call option on that stock
The potential obligation to deliver the stock if the market price exceeds the
exercise price is covered by the stock held in the portfolio.
This strategy has been popular among institutional investors in order to boost
income by the option premiums collected on writing calls.
o Straddle
Buying both a call and a put option on a stock, with the same exercise price and expiration date.
The value of this strategy is highest when the stock price makes an extreme upwards or downwards
movement from the exercise price.
Straddles are bets on volatility
Writers of straddles bet on the opposite case
A less volatile stock than expected within the span of the option premiums
o Spread
Combination of two or more calls, or puts, on the same stock with different exercise prices and or
different expiration dates
Vertical or money spread
o Same maturity
o Different exercise price
Horizontal or time spread
o Different maturity dates
o Collars
Strategy that ‘brackets’ the value of a portfolio between two bounds
Payoff diagram looks a bit similar to bullish spread
Now, you own stock, write a call and purchase a put
Bullish spread at expiration value
o Graphs
If the option prices are not in line, arbitrage will be possible
X
o C+ =S 0+ P
(1+ r f )T
, Olivier van den Wall Bake - 5510929
o Payoff is identical, therefore the initial cost should be identical
Put-call parity relationship
o The put-call parity theorem represents the proper relationships between put and call prices.
If the parity is ever violated, an arbitrage opportunity arises.
For that reason
Two portfolios always provide equal values
o The call-plus-bond portfolio
o Stock-plus-put portfolio
In the money:
o Exercise of the option would be profitable
Call
Market price of underlying stock > exercise price
Put
Exercise price > market price of underlying stock
Out of the money
o Exercise of the option would not be profitable
Call
Market price of underlying stock < exercise price At the money option
Put
Exercise price < market price of underlying stock
At the money
o Exercise price and asset price are equal
Protective put versus stock investment
o Protective put portfolio comes at a cost
Option like securities
o Callable bonds
The sale of a callable bond is essentially the sale of a straight bond to the
investor and the concurrent issuance of a call option by the investor to the
bond issuing firm.
The coupon rates of callable bonds need to be higher than the rates on straight bonds.
o Convertible securities
They convey options to the holder of the security rather than to the issuing firm. A convertible bond is in
fact a straight bond plus a valuable call option.
Therefore, a convertible bond has two lower bounds on its market price
The conversion value
Straight bond value
A bonds conversion value must equal the value it would have if you converted it into stock immediately
o Warrants
Are in fact call options issued by a firm. The difference is that the exercise price of a warrant obliges the
firm to issue a new stock. Moreover, warrants result in cash flow for the firm when the holder of a
warrant pays the exercise price
Equity can be viewed as a call option on the firm
o Collateralized loans
A collateralized loan is in a way an implicit call option to the borrower, since the lender cannot sue the
borrower for further payment if the collateral turns out not to be valuable enough to repay the loan at
some point.
Another way of describing such a loan is to view the borrower as turning over the collateral to the lender
but retaining the right to reclaim it by paying of the loan.
o Levered equity and risky debt
Investors holding stock in incorporated firms are protected by limited liability
In sense, they have a put option to transfer their ownership claims on the firm to the creditors in return
for the face value of the firm’s debt.
An argument could also be made for investors holding a call option
Financial leveraging and exotic options
o Options enable various investment positions that depend on all kinds of other securities
o They can also be used to design new securities or portfolios
They enable financial engineering, the creating of portfolios with specified payoff patterns
o Exotic options
Are variants of new option instruments available to investors.
EX
o The payoff of Asian options depend on the average price of the underlying asset
during at least some portion of the life of the option. In this case of barrier options
the payoffs also depend on whether the underlying asset price has crossed through
some barriers.
Value of a protective put position at option expiration Value of a covered call position at expiration
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