|
ABF305 Investment Management
Lecture 9
What you do not need to read in Chapter 23.
For Chapter 23, you do not need to read from page 809 ‘Credit risk in the swap market’ onwards. You also do not need to do the section on creating synthetic stock positions which is on pages 796 to 799.
An International Perspective: Exchange rate risk.
国际视野：汇率风险。
Let us say that you are a company based in Britain but you export goods to the US. Because you will be paid in USD, you need to convert this money into GBP’s. As a consequence, you face an exchange risk.
让我们说，你是一个总部设在英国的公司，但你向美国出口货物。因为你会以美元支付，你需要转换到英镑的这笔钱。因此，你面临的汇率风险。
Use a futures or forward exchange rate contract.
使用期货或远期汇率合约。
To arrive at a future exchange:
Consideration is given to the difference in the respective interest rates for the currencies involved.
The forward exchange rate is determined on the basis of an interest rate parity relationship.
‘The interest rate parity is the relationship that must exist in an efficient market between the spot and forward foreign exchange rates between two countries and the interest rates in those countries’ (Bodie, Kane and Marcus, ‘Investments’ 8th Edition).
Direct and Indirect Exchange rate quotes:
直接和间接汇率报价：
When it comes to sterling against the USD the quote is $/₤ which means the number of dollars for every ₤. This is called a direct quite because it is expressed in dollars.
当它涉及到英镑兑美元的报价为美元/₤，这意味着美元的数量为每₤。这就是所谓的直接比较，因此体现为美元。
Otherwise the quote is foreign currency/$ which is an indirect quote because it is the number of units of foreign currency for every $.
否则，该报价是外币/美元这是一个间接的报价，因为它是外币单位数量，每$。
How to determine the change in portfolio value.
Determination of the change in portfolio value can be arrived at by looking at a historical relationship such as relating business profits (as measured in dollars) to the exchange rate. You can, using historical data plot the linear relationship with the exchange rate as the x-axis and the profits on the y-axis.
See Lecture 9 Example 1 downloaded on module folder.
We are told in this example that there is a change in the portfolio value of $200,000 for every 10 cent exchange rate movement, so to offset it we need to find out per futures contract, what would be the exchange rate profit for a 10 cent movement.
How to determine the profit in one futures contract.
如何判断一个期货合约的利润。
For $/GBP futures, one contract is for 62,500 pounds. Because each contract calls for delivery of 62,500 pounds, the profit on each contract per swing of $0.10 in the exchange is $6,250. According to the hedge ratio, this means we would need 200,000/6250 = 32 contracts.
Do we sell or buy the futures contracts?
We need to think in terms of the offsetting position. If we wanted to ensure the price for a stock portfolio, then we would need to sell a futures index to ensure the portfolio price.
Textbook definitions:
‘Hedging requires investors to purchase assets that will offset the sensitivity of their portfolios to particular sources of risk.
A hedged position requires that the hedging vehicle provide profits that vary inversely with the value of the position to be protected’.
The hedge ratio is the number of futures contracts one would establish to offset the risk of a particular unprotected position. (Bodie, Kane and Marcus ‘Investments’ (8th Edition).
Sources of risk for an investment portfolio that require hedging.
需要对冲投资组合的风险来源。
Exchange rate risk.
汇率风险。
Market risk, namely from the stock market.
市场风险，即从股市。
Interest rate risk.
利率风险。
Specifics regarding Stock Index Futures.
In contrast to most futures contracts which call for delivery of a specified commodity, stock-index contracts are settled by a cash amount which is the difference between the stock index value on maturity and the futures price. Profits from futures therefore duplicate those that would arise from actual delivery of the underlying.
Another specific of stock index futures is the determination of the contract size. A contract size is determined by the stock index x a multiplier. So for example, if you were to look at Table 23.1 on page 796 in your textbook, you would see that the contract size for the S&P500 is $250 times the index.
Profit from 1 S&P500 contract
To determine the profit from one contract, it would be the difference in the futures price and the final S&P index value x $250.
So if the futures price was 1,400 and the final S&P index value was 1,405, then the profit for a long side position would be $250 x (1405-1400) = $1,250.
How to hedge a stock portfolio: Example.
Suppose that the S&P500 index has a current level of 1000. Also suppose that if the index was to decrease to a level of 975. This would represent a drop of 2.5% namely 1000-975 = 25 which as a percentage of the underlying 1000, it is equal to 0.025 or 2.5%.
Example (contd).
Let us say that you have a stock portfolio with a beta of 0.8. In terms of a loss, given the market loss as represented by the S&P500, your loss would be 0.8 x 2.5 = 2%.
If your portfolio value was $30 million, then your loss in dollar terms would be $600,000.
What this represents is for an index change of 25, your change in portfolio value is $600,000.
If the portfolio change in value is for a 25 point change in the index, then the profit for the futures contract must also be for a 25 point change in the index. The profit from one contract futures for a 25 point change in the index would be $250 x 25 = $6,250.
Where does interest rate risk arise?
The first scenario might be for a bondholder. We know that if interest rates increase the value of bond falls.
A second scenario might be for issuers of bonds. They might want to hedge any uncertainty they faced with regards to issuing their bonds.
A third scenario might be people who have funds to place and want to fix a rate of interest. This might be pension funds for example.
How to interest rate risk: Example.
利率风险：举例
In the case of interest rate risk, we will look at a bond portfolio. With a bond portfolio, what we do not want is our bond portfolio value to fall, so the first thing we will do is quantify what the fall in value is in terms of 1 basis point. A basis point is when interest rates are represented in terms of 4 decimal points. 1 basis point is therefore 1 hundredth of a percent. Or it is 0.0001.
For interest rate risk, we determine the price value of a basis point. This is shortened to PVBP. The PVBP represents the sensitivity of the dollar value of the portfolio to changes in interest rates per basis point.
Let us suppose hypothetically speaking, that you have a bond portfolio which is worth $10 million. We are told that this portfolio has a modified duration of 9 years. Using the formula covered in previous lectures with regards to determining the change in price for a bond .
For our example, if the change in yield is 10 basis points, remembering the duration was 9 years, then the percentage change in our portfolio value will be determined by multiplying the $10million by 0.90% which is: 9 x 0.0010 = 0.009
Our change in portfolio value is therefore:10 million x 0.009 = $90,000
Let us find our offsetting futures contract.
For interest rate futures, it is normally Treasury bond contracts which are traded. The underlying bond nominally calls for delivery of $100,000 par value T-Bonds with 6% coupon and 20 year maturity. These are just the bond details, nothing more.
Let us suppose that we have a future contract which has a price of $90 per $100 par value. We are also told that the duration for the bond is 10 years. Since the bond nominally calls for delivery of $100,000 par value, this means that in terms of a contract multiplier, it is $1,000.
With a duration of 10 years and a change in basis points of 10; we find the percentage change is 10 x 0.0010 = 0.01%
So the change in price is $90 x 0.01 = 90 cents.
Because the contract multiplier is 1,000, the gain on each short contract will be 1,000 x 90 cents = $900.
The PVBP will therefore be $900/10 basis points or a $90 change in yield for 1 basis point.
Let us add a slight twist to things:
If I were to tell you that the yield on short-term bonds tends to be more volatile than yields on long-term bonds, for example, suppose that you have estimated that the yield on 20-year bonds changes by 10 basis points for every 15 basis point move in the yield on 5 year bonds. Then, if you were to hold a $1 million portfolio of 5 years. How would you hedge for this position?#p#分页标题#e#
If we could summarise what we have been doing today, we have been determining the dollar change in value of the underlying asset, along with the dollar change in the value of the futures contract. As a consequence, we have been able to determine a hedge ratio which tells us the number of futures contracts we need to offset our position and so eliminate our loss.
Fixed and floating interest rate.
What you would do is engage in a swap with a swap dealer. A swap dealer will actually be a bank who will act as an intermediary. There is no change in your underlying position, you have just agreed to pay a difference in the cash flows.
Let us say that you receive income of 7% from a bond portfolio of $100 million and you swapped this fixed income into a floating LIBOR rate. If the Libor fixing turns out to be 6.5%, then you would still receive the 7% from your fixed interest, however, you would need to pay the difference between the floating rate and the fixed which is ½ % or $500,000 to the swap dealer.
How to arrive at a swap price.
The argument is as follows.
For a forward exchange under a futures contract, it is argued that an appropriate exchange for 1 and 2 year’s time
Where E0 = the exchange rate now and rus or ruk is the interest rate for each currency.
If the current exchange rate is $2.03/GBP and rus = 5% and the ruk = 7%,
Then the futures exchange for 1 year is 2.03 x 0.9813 = $1.992/GBP.
The futures exchange for 2 years is 2.03 x 0.9629 = $1.955/GBP.
The problem is that for a swap arrangement, it calls for the same delivery, namely the same exchange for the period of the swap.
It could be argued that you should add the 1.992 and 1.955 together and divide by 2 so each year, the exchange is 1.974. The argument is then that the swap price (F*) should be calculated as: 1.992 + 1.955 = F* + F*
It is also argued that both strategies namely a forward and a swap must be equally costly, it is as such argued that each strategy must be discounted by the yield curve for the dollar cash flow with is the US yield curve namely 5%.
Where you solve for F* which turns out to be 1.974.
|
