HSBC Compounds the Errors
21 March 2003
In a slight detour from corporate governance, we take a look at misleading financial advertising. We received an amusing brochure from The World's Local Bank the other day, preaching the benefits of lending them money (which banks euphemistically call "saving"). We just couldn't resist sharing our mail with you.
The article in the HSBC brochure Investment Frontier was entitled "Achieving your financial goals - become a millionaire by saving just HK$3,000 a month". Of course, the fast way would be to convert that into an even funnier currency like the Indonesian Rupiah or Turkish Lira, but let's assume we stay in the Hong Kong dollar to get our seven digits.
The bank offers us a "Case Study for Financial Planning", comparing Simon, aged 22, and Peter, aged 32, both of whom start saving $3,000 per month. Peter keeps saving till he is 57, while Simon stops at age 32. The bank tells us:
"Peter, who has not recognised the importance of saving early, starts saving HK$3,000 a month at the age of 32 for a period of 25 years - that is 15 years longer than Simon...at the end of which his total contributions will be HK$900,000, an amount that's two and a half times greater than Simon's."
Then the bank shows us this table:
| Simon | Peter | |
| Age commenced saving | 22 | 32 |
| Age stopped saving | 32 | 57 |
| Monthly contributions | $3,000 | $3,000 |
| Total contributions | $360,000 | $900,000 |
| Cumulative savings at age 57 (with interest return) |
$2,206,124 | $2,089,376 |
| Assuming yearly return rate of 6% | ||
This is what the bank says:
"Most people would think that by saving for 15 years longer than Simon at the same rate of return, Peter's cumulative savings over 25 years would amount to more than Simon's savings over 10 years.
The reality, however, is quite different. The critical factor is that Simon started saving when he was younger. This, together with compound interest and good financial planning, puts Simon way ahead even though Peter has been saving for 15 years longer."
We find that grossly misleading. As we shall show, Simon is in reality not "way ahead" of Peter - in fact, it is the other way around. HSBC is trying to persuade impressionable young savers that by saving for just 10 years, you will be better off at retirement than someone who saves for 25 years and has contributed 2.5 times as much. This is simply not true.
For the mathematicians among you, the formula for total return from investing a fixed amount $M per month at the beginning of each month for N months with a monthly interest rate of R is:
M * [(1+R)^(N+1)-1-R] / R
The three key errors in HSBC's advertorial are:
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To get the above tabled returns, you need R=0.5% per month which, with compounding, is equivalent to an annual interest rate of about 6.17% - that's more than the "yearly return rate of 6%" stated in the example. It may sound like a small difference, but over 25 years that compounds to a difference of 4.28% in returns.
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The bank fails to point out that Simon retires 10 years later than Peter - so by comparing the amount they each have when aged 57, they are not comparing the same dollars. When Peter retires in 2028, a dollar he puts in the bank (at the same interest rate) will compound to $1.819 ten years later (at aged 67), when Simon retires.
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The bank fails to point out that the real value of contributions decreases over time. If one can get 6% in the bank, then a contribution of $3,000 payable a year from now can be funded by depositing $2,830 in today's money. So comparing the total contributions of $360,000 from Simon and $900,000 from Peter is meaningless, as they are not shown in current dollars.
So let's look at what the table should have showed, to be fair:
| Simon | Peter | |
| Age commenced saving | 22 | 32 |
| Age stopped saving | 32 | 57 |
| Cumulative savings in 2028 when Peter retires (with interest return) |
$1,212,558 | $2,089,376 |
| Cumulative savings in 2038 when Simon retires (with interest return) |
$2,206,124 | $3,801,404 |
| Assuming monthly return rate of 0.5%, or about 6.17% per annum | ||
What this shows is quite simple. Simon stops saving after 10 years, while Peter carries on for another 15, so he has 72.3% more money than Simon in 2028, and the differential is maintained after a further 10 years. He is "way ahead" of Simon, not the other way around. The only trace of truth in HSBC's advertorial is that you have more time to save if you start young. That doesn't mean you can stop when you get to 32 and live happily every after.
Webb-site.com calls on the HK Monetary Authority to clamp down on this kind of deceptive advertising.
All this is pretty sad coming from a bank which currently pays 0.01% on savings accounts (up to $1m), or about 1.3% below HIBOR (the inter-bank rate). In fact, this 0.01% is probably less than the annual default risk of the bank - it implies that such a bank would only go bust once in 20,000 years if you get half your money back when it fails. If it were not for the need to make electronic payments and the risk of robbery, it would be logical to take the cash out of the bank. This is why rates cannot go negative - people would simply rent bank deposit boxes and put the cash in there instead.
© Webb-site.com, 2003
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