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401k Plan Sponsor & Participant Primer – The Risk-Return Tradeoff

October 01
17:11 2010

One of the more significant investment models developed by the academic industry goes by the name “Modern Portfolio Theory”. It attempts to provide a theoretical basis for why people invest in the various things they invest in. The 204943_9062_play_at_your_own_risk_stock_xchng_royalty_free_300theory is not causal. In its most pure form, it does not try to predict an outcome in the manner of a physics theory (although financial alchemists often try to make it do such a thing). Many practitioners believe Modern Portfolio Theory died a decade or so ago. If that’s true, it retains a very vibrant ghost.

Alive or dead, the notions of “risk” and “return” – the fundamental elements of Modern Portfolio Theory – will remain a common sense cornerstone to any prevailing investment theory. Of the two, the average person understands the latter a lot better. The “return” represents the amount of money made (or lost) on a particular investment (not including what you originally paid for the investment).

Here’s a simple example: Suppose you opened up a savings account by putting $100 in it. After exactly one year, you close the account and the bank gives you $101 back. Your return is $1 (since we don’t include the original $100 used to open the account). In this case, because we had the bank account for exactly one year, we calculate the “annual rate of return” by dividing the original investment ($100) into the return ($1) to come up with 1%.

To pound home the thought, we’ll try one more example. Say we bought 100 shares of XYZ Corp. for $10 a share and sold the stock one year later for $8 a share. We would have paid $1,000 for the stock and received $800 when we sold it. Our return would be -$200 (i.e., we lost $200 on the investment) with an annual rate of return of -20%.

Pretty straight forward stuff compared to how we define risk. In strict theoretical terms, Modern Portfolio Theory suggests the risk associated with an investment depends on the volatility of returns. Wow. A mouthful.

Said another way, let’s take two investments – your savings account and XYZ Corp. stock. Since the bank promises to pay you a certain amount (in this case, 1%), you are nearly certain to get that return on your money (and if your savings account is less than $250,000, the U.S. Government, through the FDIC, will guarantee that you get that money – at least through December 31, 2013). XYZ Corp. stock, on the other hand, makes no guarantees. It doesn’t even have to pay a dividend if it doesn’t want to. We therefore have a wide variety of possible returns. The annual rate of return of XYZ Corp. can range from -100% (you lose all your money) to infinity (you make loads of money).

Risk measures how certain an investor is of getting a return. The investor can depend on the bank paying interest on the money in the savings account. The investor cannot, with equal certainty, predict the return of XYZ Corp. Therefore, XYZ Corp. stock is riskier than a savings account. In fact, because the investor is virtually guaranteed to get the return on the money placed in the savings account, we might be tempted to call this a “riskless” investment.

Now, despite our example, one should not conclude the wisest thing to do is to always keep one’s money safely stashed in a savings account. The terms “safe” and “risk” are linked – something which is “less risky” is said to be “safer”.

Recall the savings account will only yield an annual return of 1%. XYZ Corp., on the other hand, can produce a return much more than this. In order to decide what to invest in, says Modern Portfolio Theory, one must consider both the risk and the return associated with the particular investment.

The “risk-return tradeoff,” simply stated, implies one will expect a greater return from a riskier asset. For example, would you pay more for an old lotto ticket which has already won $100 or a new lotto ticket which only has a 50% chance of winning $100? In the purely mathematical world of game theory, you would pay no more than $100 for the winning ticket and no more than $50 for the risky ticket. (The $50 is determined by calculating the average of the two possible – and equally likely – returns, namely $0 and $100, the average of which being $50.) If both tickets are winners, you get back 100% of your investment on the “sure thing” ticket, but the return for the risky ticket is 200% of your investment.

More risk, more return. The price you pay for an investment is directly related to the return you expect that asset to yield. Please note the above does not imply higher absolute prices always mean lower risk. The price we refer to is the relative price. For example, to change the lottery example a bit, suppose the old lotto ticket only won $25, but you still have a 50% chance of winning $100 on the new ticket. You would therefore pay at most $25 for the riskless ticket (it’s riskless because it’s already won the $25) and still no more than $50 for the risky ticket. In this case, the safer ticket costs less in absolute terms than the riskier ticket.

For the investor, less risk means less expected return. Savings accounts rarely outperform, say, the best start-up company stocks. Of course, on the flip side, a savings account would almost never underperform the worst start-up company stocks (which all tend to lose money). So, according to the theory, whether or not you invest in savings accounts or start-up company stocks depends on how much a loss you can stomach.

So, how exactly can we measure risk? Well, that’s an age-old question the sages in their ivy-covered towers continue to debate. Perhaps we’ll tackle that at a later date.

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Christopher Carosa, CTFA

Christopher Carosa, CTFA

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