A financial adviser whom I hold in high regard once told me that one of his biggest challenges was persuading clients to overcome their fear of losing money and to realise that, as long-term investors, they would be far better advised to invest in equities than bonds. This is despite what I could describe as the adviser's curse, quoted earlier:
We all worry about our money, and get upset if we make a loss on an investment. For a financial adviser, there is the additional trauma that the client could blame you for the loss even though your advice to invest in something could be absolutely kosher in probability terms. The problem for the financial adviser is that they are on a hiding to nothing. The client is likely to apportion at least part of the blame to the adviser if things go wrong, but to take the credit themselves if things go right. This makes the adviser even more loss-averse than the client, because of the asymmetrical payoffs. Rather than it being the reverse (as it should be in a rational world), the client has often to overcome the adviser's loss aversion. There are some notable exceptions.
Against that background, it is depressing to find advisers on this forum doing everything they can to frighten people off investing in equities.
One of the most ridiculous is this:
Imagine an investor that earns 10% on her portfolio in one year, and then loses 10% the next. The common mistake is to think that the investor would now be back to where she started. After all, the average of the two annual returns of +10% and-10% is simply 0%.
In actual fact, our investor would have lost 1% over the two years!
That’s an annual loss of about 0.5%
And the effect would have been even worse for more extreme movements. If the investor had instead gained 15% and then lost 15%, the net loss over the two years would have been 2.25%. 20% up and 20% down and the loss would have ballooned to 4% over two years.
Later, the same poster refers to prices being distributed lognormally, meaning that their logarithms are distributed normally. Translated into English, this means that the probability of a gain of 10% (over a very short period) is exactly the same as a loss of 9.09%. So why did
@Marc choose to assume a loss of 10%? Was the purpose to frighten clients off investing in a volatile asset? That is exactly the opposite of what my financial adviser friend says is the challenge with his clients.
The same objective of frightening people off investing in equities is evident in the rubbish about arithmetic and geometric means, and in the reference to the so-called "volatility drag"
A simple example will show why arithmetic means are meaningless in this type of situation. Suppose I am considering an investment returning 0% in the first year and 12% in the second year. No one would be stupid enough to say that the average return over the two years is 6% a year (12% divided by 2). Anyone with a brain in their head will at least start by calculating what return they would need each year, reinvesting the proceeds, to have 112 after two years, which is 5.83%. If they're in the honours class, they may go on to calculate what they would need to earn if the return was paid half-yearly (5.75%). The 6% is a meaningless calculation, so I don't know why anyone bothers with it.
Then we get the reference to "Volatility drag".
VOLATILITY DRAG
This unfortunate effect is due to the fact that compound annual returns are always below average annual returns.
If anything, one could interpret the latter part of this post as saying that it should be called a volatility bonus rather than a volatility drag, because the expected return under
@Marc's favoured lognormal distribution is e^(µ +0.5*σ^2). Thus, for any given µ, the higher the volatility (σ), the higher the expected return.
@Marc should therefore be looking for investments with high σ for his clients!
In saying all that, I confess that I'm not an expert on stochastic calculus. I'm sure there are some such experts who will set us both right.
