Week 7
Investing abroad:
Why not: home bias: people prefer to invest in what they know and tend to be afraid to invest in foreign
markets.
Why: Provides better diversification opportunities. however foreign exchange rate risk becomes
introduced. This leads to variations in returns related to changes in the value of domestic and foreign
currencies.
Countries are ranked based on political risk, financial risk and economic risk factors
Investing in international markets:
ADRs (American Depository Receipts)
in US If you are an individual investor in the US, sometimes it is not easy to invest in other countries.
That is why there are American Depository Receipts in the US. Banks can purchase stocks abroad and they
can issue claims on the stocks they purchased on the local stock market. So, you are indirectly investing in
foreign stocks.
- Passive investing using ETFs (Exchange-Traded Funds)
- iShares MSCI Emerging Markets You are following an index that is composed of companies that are listed
in emerging markets.
After the introduction of the euro people began to invest much more in foreign markets as exchange rate
risk was removed
Risk in developed vs emerging markets:
As expected there is much more votility in
the returns of emerging markets as there is
higher risk
-Less correlation between stocks allows for better
diversification
-Possible to expand the efficient frontier above
domestic only frontier
- Possible to reduce the systematic risk level
below the domestic only level
,Correlations across markets:
The all-country index and developed country index are highly correlated as the all-country index is market
value-weighted, meaning developed countries make up most of the weight. Up until 2007, the emerging
country index was relatively uncorrelated
-However, in 2008-2009, the correlations increased tremendously: 0.4815 was the correlation with the All
Country Index, 0.4472 with the Developed Market Index and 0.6370 with the Emerging Market Index.
-So, this is the problem of diversification: when you need it the most, when the market is crashing, usually
the diversification potential of adding additional investments to your portfolio becomes limited. If there is
a crisis, people are selling all their assets, and it does not matter whether it is in a developed market or in,
a frontier market or an emerging market.
A frontier index incudes
countries which would
not yet be considered
emerging markets
Using the Sharpe ratio they found that portfolio 3 offered the highest risk to return ratio
Difficulties in international investing
o Availability of information
o Liquidity The bid-ask spreads are usually wider. There are more implicit trading costs.
o Transaction costs
o Political risk
o Foreign currency risk (can be hedged to a large extent)
Chapter 16: Managing bond portfolios
Interest rate risk Bond pricing relationships
1. Inverse relationship between price and yield
2. An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a
decrease in yield
3. Long-term bonds tend to be more price sensitive than short-term bonds (more coupons payments impacted)
4. As maturity increases, price sensitivity increases at a decreasing rate
5. Price sensitivity is inversely related to a bond’s coupon rate (if a bond has a v high coupon rate eg 12% interest
rates are not gonna decrease it’s value by as much)
6. Price sensitivity is inversely related to the yield to maturity at which the bond is selling ( A higher yield
reduces the present value of all of the bond’s payments, but more so for more-distant payments. Therefore, at a higher yield, a
higher proportion of the bond’s value is due to its earlier payments, so effective maturity and interest rate sensitivity are lower.)
,Macaulay’s duration
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
-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
Why
If we have a zero coupon bond, the duration of that bond is equal to the maturity of the bond.
For a coupon bond, the duration of the bond will be smaller than the maturity of the bond because we
already do get coupons in the first years. Therefore, the effective maturity will be a little bit less than the
actual maturity of the bond. If we now talk about a bond with higher coupons, we get a larger weight of all
the payments in the first years. That means that the duration becomes shorter again. So, duration is a
concept that captures maturity, the relative value of the coupons relative to the par value, and the yield to
maturity.
Duration Calculations:
Y= YTM
Wt= the weight applied to each payment time is the proportion of the total value of the bond accounted
for by that payment, that is, the present value of the payment divided by the bond price.
Final formula: We have seen that a bond’s price sensitivity to interest rate changes generally increases
with maturity. Duration enables us to quantify this relationship. Specifically, it can be shown that when
interest rates change, the proportional change in a bond’s price can be related to it’s change in yield to
maturity
,Forward Contracts (made between two parties)
Forward contracts specify the delivery or sale of a security at a point in time in the future
- When shorting a stock you must borrow the asset, sell it, then return it. With futures it is just a contract
to buy/sell at a future date nd only the margin is required, no one has to own an asset to begin with
Asset currently costs $50
Short-selling: I will sell you this asset for $50 in one year
Buying-long: I will buy this asset from you for $50 in one year
If it goes down in price short benefits and if it goes up in price long benefits
Futures Contracts (contract made with clearing house between parties)
It allows people to reverse or reduce their positions. And removes counterparty risks from contracts.
Hedgers can use future contracts to protect and against risk. Eg an airline forward contract for price of oil
Open interest: total number of outstanding contracts in the market. Increases when more traders enter
Margin: you must have a certain amount of the final amount in your account with the clearing house. Gains
and losses are added and subtracted from the initial margin deposit. When the margin falls below the
required level there will be a margin call and they will need to deposit more money into the account
Basis Risk: The difference between the futures price and the spot price. Over time they will typically
converge
It is the variability in the basis that will affect profits/ hedging performance
Pricing
With a perfect hedge there is no risk so the return should equal the risk free rate
EG: investor owns an S&P fund that has a current value of $4500.
A 1 year futures contract is available for $4650. The investor hedges (shorts)
Now assume that $100 of dividends will be paid at the end of the year
S0 is initial value
is middle scenario
,Spot-futures parity theorem
example:
S0 = 1300 D = 20 rf = 4% Now assume F0 = 1345, what would you do?
In this case, according to the spot-futures parity theorem, the actual futures price should be 1332.
As 1300(1+0.04) – 20= 1332
So, there is some mispricing here since the future is $13 more expensive on the market than it
should be
To take advantage of it you would sell (short) the futures contract, however, this exposes you to
stock price fluctuations (if the price of the stock went up you would lose out)
To hedge your short position you buy $1300 of stocks financed by borrowing at the risk-free rate
You are a risk-free payoff of $13, which is equal to the mispricing of the futures contract
Because you bought the stocks you just give them to the owner of the futures contract, so price
fluctuations don’t matter your total borrowing cost was $1352, and you get $1345 + $20 dividend no
matter what
General Rules:
If the futures price is too high, short the futures and acquire the stock by borrowing the money at the risk
free rate
If the futures price is too low, go long futures, short the stock and invest the proceeds at the risk-free rate
Example: same as above but the futures price is $1319
Long future: Someone must sell to you at $1319 in one year
Short stock: borrow stock from a broker and sell for $1300 then invest @ 4% and make $1352
Then in 1 year you give broker the $1319 of shares + $20 dividends
$1352-$1319-$20=$13
, Expectations hypothesis: the futures price is always equal to the expected price. However, sometimes the
market is in contango (the futures price is higher than the expected spot price) and sometimes in normal
backwardation (the futures price is lower than the expected spot price)
Which occurs depends on who the natural hedgers are
If supply is in excess, the short side of the contract (farmers with wheat), the market will usually be
in a normal backwardation. So then, the futures price is less than the actual expected price simply
because there are so many people (farmers) that would like to hedge their price risk.
The other way around, if the long side of the contract is the majority (beer producers that need
wheat to put in their beer), the market will be in contango.
Unlike the payoff of a call option, the payoff of the long futures position can be negative: This will be the
case if the spot price falls below the original futures price. Unlike the holder of a call, who has an option to
buy, the long futures position trader cannot simply walk away from the contract. Also unlike options, in the
case of futures there is no need to distinguish gross payoffs from net profits. This is because the futures
contract is not purchased; it is simply a contract that is agreed to by two parties. The futures investor is
exposed to considerable losses if the asset price falls. In contrast, the investor in the call cannot lose more
than the cost of the option
Investing abroad:
Why not: home bias: people prefer to invest in what they know and tend to be afraid to invest in foreign
markets.
Why: Provides better diversification opportunities. however foreign exchange rate risk becomes
introduced. This leads to variations in returns related to changes in the value of domestic and foreign
currencies.
Countries are ranked based on political risk, financial risk and economic risk factors
Investing in international markets:
ADRs (American Depository Receipts)
in US If you are an individual investor in the US, sometimes it is not easy to invest in other countries.
That is why there are American Depository Receipts in the US. Banks can purchase stocks abroad and they
can issue claims on the stocks they purchased on the local stock market. So, you are indirectly investing in
foreign stocks.
- Passive investing using ETFs (Exchange-Traded Funds)
- iShares MSCI Emerging Markets You are following an index that is composed of companies that are listed
in emerging markets.
After the introduction of the euro people began to invest much more in foreign markets as exchange rate
risk was removed
Risk in developed vs emerging markets:
As expected there is much more votility in
the returns of emerging markets as there is
higher risk
-Less correlation between stocks allows for better
diversification
-Possible to expand the efficient frontier above
domestic only frontier
- Possible to reduce the systematic risk level
below the domestic only level
,Correlations across markets:
The all-country index and developed country index are highly correlated as the all-country index is market
value-weighted, meaning developed countries make up most of the weight. Up until 2007, the emerging
country index was relatively uncorrelated
-However, in 2008-2009, the correlations increased tremendously: 0.4815 was the correlation with the All
Country Index, 0.4472 with the Developed Market Index and 0.6370 with the Emerging Market Index.
-So, this is the problem of diversification: when you need it the most, when the market is crashing, usually
the diversification potential of adding additional investments to your portfolio becomes limited. If there is
a crisis, people are selling all their assets, and it does not matter whether it is in a developed market or in,
a frontier market or an emerging market.
A frontier index incudes
countries which would
not yet be considered
emerging markets
Using the Sharpe ratio they found that portfolio 3 offered the highest risk to return ratio
Difficulties in international investing
o Availability of information
o Liquidity The bid-ask spreads are usually wider. There are more implicit trading costs.
o Transaction costs
o Political risk
o Foreign currency risk (can be hedged to a large extent)
Chapter 16: Managing bond portfolios
Interest rate risk Bond pricing relationships
1. Inverse relationship between price and yield
2. An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a
decrease in yield
3. Long-term bonds tend to be more price sensitive than short-term bonds (more coupons payments impacted)
4. As maturity increases, price sensitivity increases at a decreasing rate
5. Price sensitivity is inversely related to a bond’s coupon rate (if a bond has a v high coupon rate eg 12% interest
rates are not gonna decrease it’s value by as much)
6. Price sensitivity is inversely related to the yield to maturity at which the bond is selling ( A higher yield
reduces the present value of all of the bond’s payments, but more so for more-distant payments. Therefore, at a higher yield, a
higher proportion of the bond’s value is due to its earlier payments, so effective maturity and interest rate sensitivity are lower.)
,Macaulay’s duration
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
-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
Why
If we have a zero coupon bond, the duration of that bond is equal to the maturity of the bond.
For a coupon bond, the duration of the bond will be smaller than the maturity of the bond because we
already do get coupons in the first years. Therefore, the effective maturity will be a little bit less than the
actual maturity of the bond. If we now talk about a bond with higher coupons, we get a larger weight of all
the payments in the first years. That means that the duration becomes shorter again. So, duration is a
concept that captures maturity, the relative value of the coupons relative to the par value, and the yield to
maturity.
Duration Calculations:
Y= YTM
Wt= the weight applied to each payment time is the proportion of the total value of the bond accounted
for by that payment, that is, the present value of the payment divided by the bond price.
Final formula: We have seen that a bond’s price sensitivity to interest rate changes generally increases
with maturity. Duration enables us to quantify this relationship. Specifically, it can be shown that when
interest rates change, the proportional change in a bond’s price can be related to it’s change in yield to
maturity
,Forward Contracts (made between two parties)
Forward contracts specify the delivery or sale of a security at a point in time in the future
- When shorting a stock you must borrow the asset, sell it, then return it. With futures it is just a contract
to buy/sell at a future date nd only the margin is required, no one has to own an asset to begin with
Asset currently costs $50
Short-selling: I will sell you this asset for $50 in one year
Buying-long: I will buy this asset from you for $50 in one year
If it goes down in price short benefits and if it goes up in price long benefits
Futures Contracts (contract made with clearing house between parties)
It allows people to reverse or reduce their positions. And removes counterparty risks from contracts.
Hedgers can use future contracts to protect and against risk. Eg an airline forward contract for price of oil
Open interest: total number of outstanding contracts in the market. Increases when more traders enter
Margin: you must have a certain amount of the final amount in your account with the clearing house. Gains
and losses are added and subtracted from the initial margin deposit. When the margin falls below the
required level there will be a margin call and they will need to deposit more money into the account
Basis Risk: The difference between the futures price and the spot price. Over time they will typically
converge
It is the variability in the basis that will affect profits/ hedging performance
Pricing
With a perfect hedge there is no risk so the return should equal the risk free rate
EG: investor owns an S&P fund that has a current value of $4500.
A 1 year futures contract is available for $4650. The investor hedges (shorts)
Now assume that $100 of dividends will be paid at the end of the year
S0 is initial value
is middle scenario
,Spot-futures parity theorem
example:
S0 = 1300 D = 20 rf = 4% Now assume F0 = 1345, what would you do?
In this case, according to the spot-futures parity theorem, the actual futures price should be 1332.
As 1300(1+0.04) – 20= 1332
So, there is some mispricing here since the future is $13 more expensive on the market than it
should be
To take advantage of it you would sell (short) the futures contract, however, this exposes you to
stock price fluctuations (if the price of the stock went up you would lose out)
To hedge your short position you buy $1300 of stocks financed by borrowing at the risk-free rate
You are a risk-free payoff of $13, which is equal to the mispricing of the futures contract
Because you bought the stocks you just give them to the owner of the futures contract, so price
fluctuations don’t matter your total borrowing cost was $1352, and you get $1345 + $20 dividend no
matter what
General Rules:
If the futures price is too high, short the futures and acquire the stock by borrowing the money at the risk
free rate
If the futures price is too low, go long futures, short the stock and invest the proceeds at the risk-free rate
Example: same as above but the futures price is $1319
Long future: Someone must sell to you at $1319 in one year
Short stock: borrow stock from a broker and sell for $1300 then invest @ 4% and make $1352
Then in 1 year you give broker the $1319 of shares + $20 dividends
$1352-$1319-$20=$13
, Expectations hypothesis: the futures price is always equal to the expected price. However, sometimes the
market is in contango (the futures price is higher than the expected spot price) and sometimes in normal
backwardation (the futures price is lower than the expected spot price)
Which occurs depends on who the natural hedgers are
If supply is in excess, the short side of the contract (farmers with wheat), the market will usually be
in a normal backwardation. So then, the futures price is less than the actual expected price simply
because there are so many people (farmers) that would like to hedge their price risk.
The other way around, if the long side of the contract is the majority (beer producers that need
wheat to put in their beer), the market will be in contango.
Unlike the payoff of a call option, the payoff of the long futures position can be negative: This will be the
case if the spot price falls below the original futures price. Unlike the holder of a call, who has an option to
buy, the long futures position trader cannot simply walk away from the contract. Also unlike options, in the
case of futures there is no need to distinguish gross payoffs from net profits. This is because the futures
contract is not purchased; it is simply a contract that is agreed to by two parties. The futures investor is
exposed to considerable losses if the asset price falls. In contrast, the investor in the call cannot lose more
than the cost of the option
