Series X6 Question 6.4

[Jayant]

Question X6.4 reads as follows:
An institution has the following cash outflows:
- $4.25m in one years time
- $4.95m in two years time
- $5.75m in three years time

The following government annual coupon fixed-interest securities are available:
Stock A: 10% coupon, 1 year until redemption at par, market price $103.774
Stock B: 5% coupon, 2 years until redemption at par, market price $97.293
Stock C: 15% coupon, 3 years until redemption at par, market price $120.826

(I) Calculate the nominal amount of each stock that the institution must purchase in order to exactly match its liability outgo.


Now, the solutions say that to match the last (3rd year) cashflow you need :
5.75/1.15 = $5m of stock C
which is fine if you assume that the nominal value of the stock is $100. i.e. you need 50 000 of stock C at $100 each = $5m.

But the market price of the stock is $120.826. Why is the nominal amount then not based on the market price i.e. 50 000 x $120.826 = $6 041 300 of stock C? After all, this is the nominal amount the company will need to spend on stock C to match it's cashflow.

When the question asks for nominal value, am I to assume that it is the same as par value?

 

[Stuart Underwood]

X6.4

Hi Jayant

This is called the "bootstrapping" technique. If you go on to study ST5 you will learn much more about it. If you can do this example, with just 3 cashflows, that should be more than enough knowledge of the technique for CA1.

The idea is that you match the cashflows, starting with the last one and work backwards. You do it this way so that you're investing in bonds of the correct term. Assuming the bond redeems at par, you need to use the nominal value not the market value.

This is because it's the final cashflow you're trying to match each time, whereas the market value incorporates all cashflows.

And then if you keep doing the same, allowing for the coupons you will get on the longer bonds, and keep working forwards to the 1 year bond, there is a single cashflow at time 1 so that is then easy to match too.

Otherwise it would be difficult to know what combination of coupons on earlier bonds + redemption payment you'd need.

Hope this helps

Best wishes

Stuart

Stuart Underwood
ActEd Tutor

PS This question would not be my priority for last-minute crammers, and I wish you all the best of luck!

 

[Jayant]

Hi Stuart

Thanks for the good wishes. I'm not sure if you're insinuating that I'm doing last minute cramming, but that's irrelevant. I understand the concept of starting with the last cash flow and working backwards. That's not my question.

I agree with the question in terms of the number of stock C shares that need to be purchased. What I don't understand is why the par value was used instead of the market value to determine the nominal amount of the stock required? After all, when purchasing the stock for matching purposes, you would have to pay current market prices right?

Thanks for your response.

Kind Regards,

 

[Charlie]

Hi Jayant,

I might have misunderstood your question, but I think the point that you are trying to match liability OUTFLOWS using the cash INFLOWS from the bond.

When you BUY the bond, you pay market value, but that's an OUTFLOW to you.

You are then relying on the cash INFLOWS, which will be the nominal coupon amounts (10, 5 and 15 according to the bonds given) and the redemption value (100), to match your liability OUTFLOWS.

So once you are holding the bond, it doesn't really matter what the market value of it is (assuming you're not planning on selling it) - all that matters is the (pre-specified) nominal amounts that you'll receive on it.

I hope that helps!

Charlie

 

[Jayant]

Thanks Charlie. Makes sense now. I understand Stuarts response also now. Thanks Stuart.

 

[Stuart Underwood]

PS Jayant, no that's not what I meant. With the CA1 exams today and tomorrow, I just didn't want people who are doing last minute cramming to worry about this question ... so many more frequently examined topics than this!