Finance Case

Q1 Bond duration

Calculation of durations for five bonds is shown below. (2 marks each duration)

Portfolio duration

So the new portfolio will have a duration of 7.009 + 1 = 8.009 years (rounding is allowed). (1 Mark)

Adjust the portfolio weight with solver to achieve target duration

The weights of updated portfolio depend on the outcome of solver function. There are many combinations. Markers will check the constraints in solver of the spreadsheet submitted by group members. 4 Marks: 1 mark for correctly set constraints; 1 mark for the target duration; 1 mark for discussion about the change in portfolio weights; 1 mark for discussion about the transaction cost of your strategy, such as total trading volume and liquidity premium of different series.

Q2 Hedging with put options

1. The bank will lose in the cash market if 3 month (cash) BAB rates increase in October 2010 from current levels. As a hedge, the bank should buy a put option on March 2011 BAB futures. If interest rates do increase in the cash market, the futures quote will similarly decrease (implied yield increases) and the long put position will increase in value. If the bank offsets its put position in February by selling the put option, it should profit, which could be used to offset the increased cash market borrowing cost.

2. Option value = intrinsic value + time value

Intrinsic value of put = Max (X – S, 0 ) = Max(93.75 - 93.64, 0) = 0.11 (in %)

Therefore, time value = option value (premium) – intrinsic value = 0.44 - 0.11 = 0. 33 (in %)

3. Cash market

Initial rate on Oct 28 2010= 5.79%; rate on Feb 18, 2011 = 6.43%, a loss of 0.64%

If we consider the loss in dollar amount, it is shown as below.

Cash market borrowing amount = 10,000,000/(1+0.0643*90/365)=9,843,926.57

Loss in cash market = 10,000,000/(1+0.0579*90/365)-9,843,926.57=9,859,242.43-9,843,926.57=$15,315.86

Options position:

‘A Guide to the Pricing Conventions of ASX Interest Rate Products', published by ASX (SFE)

http://www.sfe.com.au/content/sfe/products/pricing.pdf

A 90 Day Bank Bill option with an exercise price of 92.75 and a premium of 0.44% pa would be valued as follows:

Futures contract value at 93.75 (6.25%) = 1,000,000/(1+0.0625*90/365)=984,822.93

Futures contract value at 93.74 (6.26%) = 1,000,000/(1+0.0626*90/365)=984,799.02

Difference (value of 0.01% of premium) = $984,822.93 – $984,799.02 = $23.91 (approximately $24)

Premium paid for the option = 44 X 23.91 = 1052.04 per option.

The face value of borrowing is 10million, so the bank needs to pay 10,520.40 option premiums.

On Feb 18, 2011, the bank's option position can be either exercised or squared (sell the options) because options traded in SFE is American style. The bank has to select the choice which provides more cash inflow.

If exercising the options, the profit/loss would be the intrinsic value of these put options, Max(X-S,0)

Intrinsic Value=Max(10,000,000/(1+0.0625×90/365)-10,000,000/(1+0.0655×90/365),0)=Max(7,169.20,0)=7,169.20

0.0655 (6.55%) is the spot price (implied i/r) of 90day BAB futures, 0.0625 (6.25%) is the exercise price (implied i/r) of the option on 90day BAB futures.

If selling the options (squaring the position), the profit/loss would be 34 X 23.91 X 10 = 8,129.40 > 7,169.20, so the bank should sell the options.

The net loss from option trading is 10,520.40 – 8,129.40 = 2,391 (ignore the different timing of these two cash flows)

Effective borrowing cost

Considering the loss in option trading, net cash borrowed = 9,843,926.57 – 2,391 = 9,841,535.57

Effective cost of borrowing = (10,000,000/9,841,535.57-1)×365/90=0.0653=6.53% (approximately, 6.43% + 0.10%, cost of cash market + loss