Friday, 3 February 2012

Accounting Ratios Are For Accountants, Not Insight

One of the many variables our accountants track is the average weighted selling price (AWSP): the loan-amount-weighted-APR. This varies slightly each week even in the most stable of times, especially with a pricing engine as sensitive to as many customer-centric variables as The Bank's, but no-one has a good idea of how much variation is just "BAU" ('business as usual") and when to start wondering if there's something going on on the outside, Mr Jones.

I'm wondering if we should even be tracking these kinds of accounting ratios at all. The AWSP and the ALA (average loan amount) are more-or-less inversely related: put up the APR and the amount borrowed goes down. (Who knew?) But when you look at what happens, it's not what you think that happens. You think that when we put the prices up by 10%, almost everyone knocks 10% off the amount they borrow. Not so much. In fact, not at all. Very few people take loans for some random amount like £5,237: they take loans of £4,000 or £5,000. The distribution of loans by amount is not normal, but has spikes at the round thousands. Almost no-one takes a loan for £18,000 and a fair proportion take loans of £2,000. And this is true no matter what the prices are.

I'll just say that again, because I can guarantee you didn't get it. You can change the prices all you want, and the peaks will always be at round thousands and multiples of six months in the loan terms. What really happens when we put prices up? A 10% in increase in APR from 10% to 11% on a £10,000 loan over 60 months makes a difference of £5 a month to the repayments. Most people can afford that, if they can afford the original amount in the first place. That's one reason why things don't change much for a building society with a fairly simple rate structure when it bumps up its APR's. However, the pricing models The Bank uses don't usually impose a constant increase on everyone. The changes are obtained by changing propensity curves which can make some hefty differences to some people and very little to others. You might have thought you were going to pay £220 a month, but actually it turns out that now you're going to pay £260. That's a week's petrol for the car for a lot of people. Decision time.

Many other people will be unaffected. I think (because we don't have research - yes, I said: "we don't have research") that some people make a big adjustment - instead of buying a second-hand latest-model car, they buy a second-hand previous-model car that's perhaps only six months older, because that knocks at least £1,000 off the price of even small cars (and that's my Top Tip for saving money when buying second-hand cars) - while some people abandon the project altogether because it's not the sort of project you can save £500 or £1,000 on.

Over half the personal loans made every day are to re-finance other debt, and maybe some people, faced with a higher price for the whole lot, go back one more time to the Bank of Mom and Dad to ask for help on the last £1,000. There's undoubtedly a rounding effect in the intial amount. The project (new TV, new kitchen, wedding, new floors) might cost, say, £8,250 and many people will round up to £9,000 so they can get the TV / holiday / new sheets / some other bunch of stuff they've been putting off for ages, as well. When we put the price up on them, they shrug, borrow £8,000 and fund the last £250 from a credit card or cash flow.

Take 2,000 of these random decisions a week and it smooths out. So the accounting ratios paint one picture, while the detailed MI shows something else. Accounting figures are accurate, but don't provide insight: MI is often slightly inaccurate, but provides insight. (Inaccuracy is fine, as long as it isn't misleading.)

I've been careful to call the AWSP and ALA "accounting ratios" rather than "statistics". Technically, accounting ratios are statistics (symmetric functions of observed values of random variables). Emotionally, they aren't. I have a prejudice that a "statistic" ought to do two things: it should tell me about the distribution, and it should be about something physically or commercially meaningful. AWSP sounds as if it should be commercially meaningful, but I'm no so sure. Because loans are about money, and you think all money is the same, I'll use a different example.

A record label could report the "average price per CD" (APCD). Under certain circumstances, it seems that might be a meaningful indicator. When it changed, you would still need to find out why. Did less people buy from "new release premium" label, or more people from the "new release budget" label, and why? No hot new releases this month? Was one of the budget releases was favourably reviewed on Radio Three? Perhaps the month's hot new release was on a competing label, so no-one bought much from yours. Or maybe the online server went down for two days, and since that's where your premium sales are, that's why the APCD dropped. Or maybe Amazon are making a point to you, which you've now understood. Or maybe a hundred other things because that's what business is: a thousand details that don't make a complete picture.

The accountants won't stop reporting the ratios, but the MI team, if there is one, should start reporting something more useful: the details of the product / price mix and how that changes. Or whatever other mix variables you need to look at to explain the make-up of some critical line.

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