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

Huh?

[tombee.livejournal.com]

It looks like they're giving you lots of money!

For a start, that looks too wierd for banks to sell to normal people. Do you mean, if Y>X they are giving you (£7000) _Plus_ 75% of teh excess nominal return on teh FTSE? how much are you giving _them_?

You can get a rough idea of the nominal market yield on a 4 year bond in a year's time by saying:

(current 5 year forward yield +1) ^ 5 = (current 1 year forward yield + 1) * (current 4 year forward yield +1) ^ 4

All net of tax as appropriate.

The option itself is tricky- as a fair price would a) depend on implied volatiliy for 4 out of the next 5 years, and b) in order to work this out, you need a realistic (and accurate) model for FTSE movements. If you had done martingales and financial models, you'd have learnt an unrealistic one (Black Scholes / Log wiener process). If I knew what the more accurate models were I probably couldn't tell you :P

Bear in mind that the FTSE 100 is based on market prices, and therefore only relates to capital return: it doesn't give you total return (ie capital + dividend income). I think. You can get (CURRENT) income yield on dividends from a Financial Times.

You can probably also find appropriate 5 year put option prices in the FT (this being the price of the option to sell a nominal amount of stock at a known price in the future if you want to).

I think that this would then be all you need to start "constructing an equivalent portfolio"- which is the general idea when trying to solve this sort of problem. Essentially, you work out the cost of generating the cashflows using available market instruments whose price you know (think in shapes- this is a straightforward exercise for a competent mathematician). However, as I'm not 100% sure what your deal does, I don't propose to do this now.

In any case, my charge out rate would cause you to temporarily stop breathing.

Hope this is of some assistance :)

Tom

Re: Huh?

[fivemack.livejournal.com]

Hi Tom.

They want £10,000 for this deal, and sell it as 'up to 30% can go in a bond, down to 70% in this guaranteed-no-absolute-loss stock market thingie'. Yes, I got the maths wrong, I get £7k back in any case, and if the FTSE has gone up 10% over the five years, I'd get 1.075*£7k.

So in worst scenario where FTSE has gone down (eg the situation I'd have been if I'd bought the equivalent to this deal five years back and it were maturing now), I have, in 2010, £7000 + £3168*risklessreturn^4.

I'm not sure how the bank actually implement the deal. I suspect they put the whole lot in an index-tracker reinvesting dividends, and are betting

a) FTSE return is >7% (3168 is 7%-tax) over one year
b) FTSE return over five years with dividends reinvested (thanks for that point!) is positive

Which is a bet I'd be moderately prepared to take. I don't have usefully formatted time-series data on ftse100, but I think the five-year returns have been reasonably positive in the medium past (though dreadfully negative for a while recently).

Thanks for explaining the details and the jargon,

Other Tom

[(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.