Tom is under-educated

[fivemack]

I can't remember whether it was Further Group Theory or Number Theory that I took when I could have been taking Martingales and Financial Mathematics. Both have been useful in my life, but in this situation appear less so.

My bank wants to sell me the following deal:

* Let X be the current value of the FTSE 100 index
* Let Y be the value of the FTSE 100 index on 15 June 2010
* On 15 June 2006, they give me £3168
* On 15 June 2010, if Y<X, they give me £7000. If Y>X, they give me 0.75*((Y-X)/X) * £7000

All the figures for money the bank gives me are after tax.

This looks to me like a classic sort of option-pricing problem. How do I figure out what a fair price for the deal ought to be?

Current rate for a five-year bond is 4.0% after tax; I'm sure there's some sort of bond-lengthening derivative equivalent to 'I will pay you on 15 June 2010 the amount of money you'd have then if you'd bought the best-on-the-then-market 4-year bond in 15 June 2006', but I don't know what it would be called or what it's value is agreed to be.

Equally, I'm sure that long-term FTSE futures are a standard derivative, but I don't know how to find the relevant valuations.

Comments

[(Anonymous)]

These deals are often not good value.

The deal on the £3,000 part is obviously good. Compare to the best online savings account you're making about an extra £40.

The deal on the rest is suspect. As a best estimate, equities will probably return about 7-8% pa. Of that, about 3% is dividends so capital growth is 4-5% pa. You get 75% of that i.e. 3-3.75% pa. As a crude estimate, the optionality is probably worth about 0.5% pa. So I reckon the expected net return is 3.5-4.25% pa.

What you have to watch out for is averaging at the end of the term. Many bonds like this average over the last year. That knocks half-a-year off your investment term. So, for example, if you have decided that the expected return is worth 4% pa net and there's averaging over the past year, this reduces the return to 3.6% pa net.

Another point to bear in mind is that often these bonds don't have a penalty-free surrender option.

I have never seen a bond of this nature that I think offers good value for money. You always have to be suspicious why the bank is offering you a guaranteed good deal on the £3,000 - it's because they expect to make good profits on the rest.

[fivemack.livejournal.com]

Aha! Thank you, you may well have saved me substantial money, although reinforcing my belief in the fundamental dishonesty of bank-tied financial advisors.

The bond does average over the last year; the advisor suggested that this reduced risk if I happened to be selling out during a slump, and I didn't spot that it had quite so obvious an effect on return were everything not slumping. Early surrender is, indeed, not merely penalised but forbidden.

Please accept this Little Grey Rabbit award for expertise in the spotting of concealed weasels.