## Saturday, 8 October 2011

### Anatomy of a convert - in the interest of fairness

You just got a £1,000 bonus and would like to invest it somewhere to help towards your kids' education in the future.  You're naive so don't know about risk adjusted return yet.  You pick up a copy of the Financial Times and read about investment opportunities.  One story tells of a man who bought drilling rights for £10,000,000 and has struck oil.  Those rights are now worth £40,000,000.  Another story tells of last week's lottery winner who, with £10 managed to get a jackpot of £18,000,000.  A chart shows you that the S&P index was at 1,270 at the start of the year and now languishes at 1,155.  Your bank manager tells you if you give her the £1,000 get £5 credited to your account each month.

If we pretend for a moment that your £1,000 is enough to allow you to participate in any of the above ventures, then you might ask yourself: which one would give me the most money for the investment.  (As noted above, this isn't actually the question you should be asking yourself - you ought to be asking yourself which investment gives me the most new cash given my risk appetite).

Interest rates are just ratios.  Ways of comparing how much additional cash you'd get for a nominal amount of, say £1 invested in a venture.  With the oil rights, you get 400% return, with the lottery 180,000,000% return, with the equity index investment, you get -9% return (you lose that much of your capital, in other words) and with the bank account each month you'd get 0.5%, making approximately 6% in a year.

To really be fair, you'd like to know how long it takes for those investments to pay off as they did.  For the bank account, you get 12 monthly payments.  For the market, it took 10 months to get that far, and for the oil drilling company, ten years.  For the lottery ticket, it took only 1 day.  To re-capitulate,  you started by being fair to the investment by asking how much a nominal amount (£1) invested would return to you, then you try to be fairer still by adjusting for the period of time you need to risk your capital.  This second step is akin to viewing the investments across the same nominal time period (let's say one year).  All you're doing is scaling the final cash returns by assuming a nominal investment for a nominal period.  The annualised return for the oil investment is therefore 40%, for the lottery investment 65,700,000,000%, for the stock market -10.9% and for your bank, 6%.

These simple multiplicative steps in the name of fairness allow you to reduce the noise, to get closer to making an investment decision.

### Anatomy of a convert - interested?

Interest has its own interest - cultural, historical, mathematical.  In this post I'd like to point out the vague irrelevancy we like to attribute to it in our everyday lives. Interest rates for loans to the safest bet have most often been somewhere around the 5% level, give or take. I think for many people this is psychologically around the 'fee' scale - we're all used to banks and other money institutions (pension providers, insurance companies, etc.) charging fees with are in the same ball park.  We are also mostly dimly aware of the role of inflation on money - we all dimly know that the meaning of 5% is itself in some general way clouded or constrained by the inflation level, so that gives us an even further excuse to consider the difference between, say 5% and 5.5% as not significant.

For banks and those dealing with fixed income products, like bond traders, their discrimination levels need to be a lot finer.  The reason is because they're usually applying it to much larger sums.  The only time in most of our lives where we get to play with large sums is when buying a house.  Here, we often come to appreciate the difference in meaning from a 5% payback rate and a 5.5% payback rate.  What we're doing, in our heads, is spelling out the meaning of that 0.5% with respect to a large sum.  Say our house costs £100,000.  Then that 0.5% amounts to £500.  If that was an annual additional payment, then the corresponding monthly payment would be about £42, or a meal for two in a restaurant.  Whereas if you're buying £100,000,000 worth of a convertible issue, then that 0.5% amounts to half a million pounds.  And if you earn less than a pound per day, that 0.5% is the least of your worries.