Using D to assess the interest rate risk of a financial institution's balance sheet
Point 1. A business is 'insolvent' when it has negative equity, which means that its liabilities exceed its assets. This point is relevant to the following 'mini case study'...
Point 2. Most non-financial businesses, such as retailers, wholesalers and manufacturers, finance 'real' assets (buildings, equipment etc) with a mixture of liabilities (notably debt, which is borrowed, interest-paying funds) and equity (funds contributed by the owners). From an accounting viewpoint, the balance sheet looks like this:
Liabilities $x Real assets $(x + y)
Looking at this balance sheet in a different way, it can be seen that:
Equity = Assets - Liabilities
A financial institution such as a bank differs: it funds financial assets (interest-earning assets) with interest-paying liabilities. That is, it has interest-paying instruments on both sides of the balance sheet. Because depositors are usually unwilling to invest money with a bank for a long period, whereas many loans on the other side of the balance sheet are often relatively long-term assets, there may be what is called a maturity 'mismatch' between the two sides of the balance sheet But, because Duration better measures the price risk/market risk of financial instruments, the impact of the mismatch is measured more appropriately by the D of assets versus liabilities.
Below is an example of part of a bank's simplified balance sheet, which shows a high degree of mismatch in maturities of liabilities and assets, respectively:
CD (90 days remaining maturity)1 $1,760.922million
Fixed Deposits (1 year, fixed rate)2 $200.000million
Bonds issued (5 years)3 $300.000million
Business loans (4 years average maturity)4 $500.000million
Housing loans (10 years average maturity)5 $1,800.000million
$1800 million face-value, at rate of 9% p.a. (A CD is like a Promissory Note).
A 1-year term deposit, total $200 million deposited. Both the principal and interest are repayable at maturity. The interest rate is 10%p.a.
Par bonds, paying coupons half-yearly at 11% p.a.
Term loans repayable at the end of each quarter at a fixed rate of 14% APR
Term loans repayable at the end of each half-year at a fixed rate of 12% APR
(a) What is the current value of equity, E?
(b) What is the Duration of each of the above five balance sheet items? [HINT: only three D computations should be needed]
(c) Determine modD for each of the above five balance sheet items.
(d) Determine the approximate modD of the asset 'portfolio' A (i.e. total assets are a portfolio of two individual assets).
(e) Determine the approximate modD of the liability 'portfolio' L (i.e. total liabilities are a portfolio of three individual liabilities).
(f) Explain if the value of equity E is adversely exposed to (i) a rate rise or (ii) a rate fall, and why this is so.
(g) By adapting equation (6.3a), compute the approximate change in the value of equity, that is DE, for a rate change of 50 basis points across all assets and liabilities
[HINT: DE ≈ DAportfolio - DLportfolio]
(h) Determine what approximate size (and direction, + or ?) of interest rate change would be required to just make this financial institution insolvent?
You have recently commenced employment as a graduate recruit with Pipco Securities Co, whose CEO is Charlie Dickens. You were recruited by the HR manager, Sackin Tondulker, who has placed you in a division where your work supervisor is Lim Tian Pan. Mr Lim has just briefed you on your first job, which is to design a suitable futures hedge for a wealthy client who is planning to buy $20 million face value federal government T-bonds when they are issued in 2 months' time with maturity of 10 years (based on today's market yield, the price at issue would be par if there are no rate changes during the next 2 months).
The federal Treasury has announced that the bonds will be issued with 8% p.a. coupon rate (payable half-yearly) and the issue price will depend on the relevant market yield on the date of issue. At present, the ASX quoted price for the 10-year standard bond contract is 92.0, settlement in 2 months' time (on the same day as the new bond issue).
The client wants to ensure that she does not pay more than par for the new bond.
a. Your supervisor has asked you to design a suitable futures hedge and write a brief paper to the client, explaining how the hedge will work, assuming you enter the contract 'now' and settlement is in 2 months' time [show supporting computations, assuming (for illustrative purposes), that there is a 0.3% p.a. unfavourable rate change between entering the contract and settlement. Assume if necessary that there is a $2,800 deposit to enter each standard contract].
b. What main warning should you give your client about the nature of futures contracts? [show supporting computations assuming, for illustrative purposes, that there is a 0.3% p.a. favourable rate change, in the opposite direction of the rate change in part a. above].
You want to hedge against a fall in interest rates. Today, Q is 95.0 for a 10-year standard bond futures contract, to be settled in 6 months' time. Alternatively, for a call option on the same bond futures contract (that is, with expiry date in 6 months' time), the premium is 0.54%.
(a) (i) Assume interest rates move down 1% between 'today' and the date of expiry/exercise/settlement: What would be the 'payoff' for a futures buying position if rates move down by 1% p.a. between 'today' and settlement?
(ii) Draw the payoff diagram for the relevant option that you could use as an alternative to the futures position in (i).
(b) (i) What would be the payoff in (a)(i) if rates move up 1% p.a. between 'today' and settlement?
(ii) Draw the payoff diagram for your (a)(ii) option if rates instead move up 1% p.a. between 'today' and settlement/exercise date?
(c) Use your above answers to compare the main advantage and disadvantage of using futures vs options. [no more than 40 words]
For the share option whose computations are performed in the end of this TOPIC GUIDE, explain briefly why the Put is worth more than the Call (that is, why would someone be willing to pay more for the Put than the Call?).
NOTE: In answering questions 5, 6 and 7, most calculations can be done via the supplied Excel program "BANK5014-SP5-2012-Option-calculator". However, sometimes additional explanations are required.
On 9 September 2012, ANZ Bank's shares were trading on the ASX at $19.94. On that same day, the ASX was quoting ANZ's Call option expiring on 24 November 2012, with an exercise price of $21.50. Research shows that the yield on government securities is 6% p.a., with about 2 to 3 months to maturity (quoted on an APR basis, compounded twice per year) and ANZ's dividend yield is 6.44% p.a. (assume compounded once per year), with the volatility of ANZ returns, being 25.1% p.a. (measured via the standard deviation).
What is the 9 September theoretical value, C, of a Call option, on an ANZ share with the above characteristics?
What is C if things are the same as in part a, except that the Exercise price is $19.50? Explain why this is so.
What is C if things are the same as in part a, except that expiry is:
(i) 29 September? (ii) 27 October?
Explain, briefly why, in part c(i) and (ii), C is less than in part a?
Assume in part a. that the risk-free rate is greater than was originally the case. Show the effect that this has on C. Explain why this is so.
Assume in part a. that share's volatility is greater than was originally the case. Give an example of the effect that this has on C. Explain why this is so.
Assume you are an options trader, that is you are buying Calls or Puts to try and make profits as a speculator. Based on your previous answers, looking ahead say 3 months to 6 months, what relevant variables seem to have most impact on options prices?
Assume all other factors are held constant, but a company then starts to pay dividends.
(i) Use a suitable computation to show what impact this has on the value of a Call?
(ii) Can you explain why this is so?
[hint: you might be able to use some of the theory from Business/Corporate finance]