Thinking about catching a falling knife? Do the math first.

After the recent stock market rout, a friend contacted me to get my take on some “financial advice” he’d received from his broker. The fellow had suggested my friend take advantage of falling prices to invest $10,000 in the stock market for a “projected” 8% return. Should he do it?

Now, every time I hear advice like that, I am reminded of that great quote in Fred Schwed, Jr.’s book, “Where Are the Customers’ Yachts?”:

“Speculation is an effort, probably unsuccessful, to turn a little money into a lot. Investing is an effort, which should be successful, to prevent a lot of money from becoming a little.

Let’s look at the math behind this problem for a moment. My friend was being asked to invest $10,000 of his hard-earned savings for which, in return, he ‘might’ get $800 in profit (before the broker’s fees!). First of all, the best performing market in the last 10 years has been the US stock market. The annualized ROI for the S&P 500 since January 2006 has been 6%, and for the tech-heavy NASDAQ, 10%. So 8% is already on the high side for the market my friend is talking about (not the US).

The volatility of the equity market in question is about 20% (23% actually). Even assuming normally distributed returns—and nothing about the recent returns is normal—the probability of earning 8% with 20% volatility is only 65%. But before responding, I asked him a question that he had evidently never been asked before. 

How much can you afford to lose?” I asked. 

Ten percent. Maximum.” he responded.

When you say ‘maximum’, what confidence level are you thinking of?” I added.

Very high, like 90% sure. This is my rent money for the next six months!” he replied.

Well, then I’m afraid this investment idea of yours is too risky for you. At 20% volatility, you can only have 82% confidence of not losing more than 10 percent of your investment. If you require 90% confidence, then you need to find an investment with just 8% volatility. At 20% volatility, there is still an 18% chance you will lose 10% or more of your money on this investment. In fact, at 20% volatility, you can only be 90% confident that you won’t lose more than 17.64% of your money,” I informed him.

So, stop dreaming about the long weekend in Bali this 8% ‘could’ get you while still being able to pay your rent, and focus instead on the real 18% probability that you will have to move out of your current apartment earlier than you planned,” I added.

My friend isn’t going to Bali. I do give him credit for the 90% confidence he required to make the investment, as this is certainly what made the math so clear to him—and the decision not to invest that much easier to accept. It also tells me he was thinking like an investor, not a speculator.

Olivier d'Assier

Olivier d'Assier is Head of Applied Research, APAC, for Axioma and is responsible for generating unique regional insights into risk trends by leveraging and analyzing Axioma's vast data on market and portfolio risk. d'Assier's research helps clients and prospects better understand and adapt to the evolving risk environment in the Asia Pacific.