This article was posted on Thursday, Aug 01, 2019

Continued from Part 2 . . . Diversified Coin Flip Time goes by.  Uncle Fred offers to divide your retirement account into two equal parts (Part A and Part B) and conduct a separate coin toss for each half. Whether heads or tails, the results of each coin toss for Part A will be limited to one half of the (former) portfolio.

When the coin for Part B is flipped it, too, will come up either heads or tails. This constitutes the gain or loss on the other half of the original portfolio. If you accept Uncle Fred’s offer, you will have two uncorrelated portfolios. Whatever happens when the coin is flipped for Part A has no effect on Part B.

Now, the math changes slightly. Instead of having, for example, one $100 retirement account with two possibilities (heads or tails), we now have two $50 accounts with four possibilities (see chart, below).

Flipping a head for Part A still yields a 30% gain, but only for the “A” half of the portfolio. Similarly, a tails results in a minus 10% return, but – again – only for the “A” half. So the math for Part A would be thus:

Heads would return +$15 (30% of $50). Tails would return -$5 (10% of $50). Combined, this example would result in a gain of $10 (+$15 and -$5) for that half of the portfolio.

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Then the process is repeated with Part B. The sum of gains and / or losses on Part A and Part B constitutes the total portfolio return.

The effect of diversifying the one coin-toss portfolio into two will be to have four prospective results. Each of the four possibilities is equally likely.




Bernstein writes, “Outcomes 1 and 4 are the same as they would be in a single coin toss, with the original returns of +30% and -10%, respectively. However, there are two additional possible outcomes, in which the two tosses result in one head and one tail. The total return in these cases is 10% (one half of +30% plus one-half of -10%).

Since each of the four possible outcomes is equally likely, and in a representative four-year period you will have one of each outcome, you find that your account will increase by a factor of:  1.3 x 1.1 x 1.1 x .9 = 1.4157

Being handy with numbers, you calculate that your annualized return for this two-coin-toss sequence is . . . . [about 9%] . . . which is nearly a half percentage point higher than your previous expected return of [about 8.5%] with only one coin toss. Even more amazingly, you realize that your risk has been reduced.” With the single coin toss there were only two possibilities: you were either going to win 30% or lose 10%. Over a long enough period of time, half of the throws would result in a loss for you. That’s a 50% loss ratio. With two separate coin tosses [one for Part A and another for Part B], there are four possibilities, only one of which results in a loss: a 25% loss ratio. Bernstein continues, Wise old Uncle Fred has introduced you to the most important concept in portfolio theory: “Dividing your portfolio between assets with uncorrelated results increases returns while decreasing risk.”

 We discussed positive and negative Deflation in April. This led to the Direction of Interest Rates in May, and Reversion Towards the Mean in June. Diversification and the possibility of (a) higher return (b) with less risk was July’s focus. Given, as we’ve seen, that lenders are increasingly requiring borrowers to demonstrate liquidity at least equal to 10% of the requested loan amount, it’s probably time to develop an overview of what an experienced apartment investor might reasonably expect from a new-to-her liquid portfolio. 

The Horse or the Saddle?

Very often, there are two or more elements to a purchase process and the decision must be made, which to buy first, the horse or the saddle? Obviously, it’s the horse. You can use a horse without the saddle, but a saddle without the horse just clutters the closet.

The Horse

This month, we’ll review the use of the Compound Annual Growth Rate (CAGR) as a measure of expected return and the standard deviation (SD) as a measure of risk. To simplify the examples, we’ll apply these investment measures to a flock of laying hens. In subsequent months, we’ll continue using CAGR and SD, but change our application to the three major asset classes: bonds, stocks and income properties. If CAGR and standard deviation works with flocks of chickens, they’ll probably work with most other kinds of investments. 

Once we’ve agreed on supportable CAGRs and SDs for each of the three major asset classes (bonds, stocks, income property), we’ll examine one or two sample portfolios and try to get a sense of how these diversified portfolios have performed over the last several decades. As always, it’s important to remember that what happened in the past does not forecast what might happen in the future. Every market has multiple variables, which as a group, do not often sync with historical markets so once again, the past is not a forecast of what might happen in the future. 

Data points are required before actionable trends reveal themselves. These points are freely available in the historical registries. As always, Google is your friend. Some data goes back over 100 years. If more than 100 annual data points are needed, the researcher can use monthly records. In that event, 100 years of data would provide 1,200 data points. That should be enough for almost anything we’re likely to do. 

The minimum number of necessary samples varies with the task. Sometimes, acceptable analysis can be done with only ten years of annual data. Often, more than ten years of data are desirable. In our case, we’ll be looking at data going back to 1970, which gives us 48 annual data points (not 49, because 2019 isn’t over yet). That’ll probably be long enough to have established an expected growth rate (CAGR) and a likely risk spectrum (SD). 

The results do not imply certainty. There is no “Oh, if that happens then this will unfailingly follow.” Regardless of the number of data points, certainty is not a sure thing. There’s always an outlier somewhere: even the most beautiful Prom Queen doesn’t always marry the handsomest boy.

What we’re thinking is that with those 48 annual data points (1970-2018), it might be possible to develop an idea of what a given investment may do in terms of (a) likely return and (b) probable safety. Or, in other words, what would be the CAGR (Compound Annual Growth Rate) and what would be the standard deviation (SD).

In terms of growth rate, higher is better. Duh. Over time, even tiny disparities amount to significant differences. $10,000 invested at 5% annual interest for 45 years (i.e., from age 20 to 65) compounds to $89,850. At 4.7%, the terminal amount would be $78,995. That reduction of 30 basis points in return made more than a 10% difference in final values. 

But higher is good only if it really happens, and that’s where Ms. Standard Deviation puts on her smile and walks through the doorway.

The Horse, Continued

One SD is defined as the range about the average return containing 68% of the data points, with half the data points being beneath the average return and the other half being above. Relative to any given asset, those two figures will reveal (a) how much we’ll get (CAGR) and (b) how likely we are to get it (SD). Their importance is that if we knew what they are, we’d know what two-thirds of our future is going to look like. That’s quite a horse, isn’t it?

Suppose, for example, a large flock of laying hens was being considered for purchase. The chicken appraiser (“And what does your husband do, Dear?”) analyzed the data and for the last 48 years (since 1970), the records show that the average hen laid 200 eggs per year. In this case, the annual number of eggs is the CAGR. The appraiser then passes that information on to the prospective buyer, who understands how standard deviation works: two-thirds of the events will cluster around the mean, half below and half above. 

The value of the standard deviation is in helping to form reasonable expectations. In any given year, Ms. Standard Deviation shows that this flock can be expected to produce between 200 minus 34% (i.e., 200 minus 68, or 132 eggs) and 200 plus 34% i.e., 200 plus 68, or 268 eggs). 

Another slightly less precise but possibly quicker way of doing the math is to divide the mean by 3 and multiply by 2. Example: 200 divided by 3 = 67 x 2 = 134. That gives us the approximate lower range of the Standard Deviation. 

To get the upper range, divide the mean by 3 and multiply by 4. Example: 200 divided by 3 = 67 x 4 = 268. It’s not quite as precise because fractions are rounded, but it can be done in your head.

The Lower the SD, the Safer  

If another flock was studied and also found to also lay 200 eggs a year but this flock’s production had a SD of 3, meaning that two-thirds of the time the annual production of eggs for each hen would be between 194 and 206. Which flock would a risk-conscious egg farmer select as his production staff?

That is an important concept: the smaller the SD, the safer is the investment.

The standard deviation is not restricted to laying hens. People can, in fact, use this simple statistical analysis to compare assets against each other and to form an opinion on which alternative better suits their needs. For example, Asset 1 may give a higher return, but at greater risk. Asset 2 may have a lower prospective return, but with less risk. There is no right or wrong here. There is only the issue of which portfolio characteristics might be suitable for which investors.

See the cautious guy on the porch swing, the one who’s trying to remember where his wife hid the Jack Daniels? Part of his mind is thinking, “I’d like to make as much return as I can, but I’m 87 years old and Edna is my fourth wife. And she’s older than me. Neither she nor I care anymore for drama, and we can’t absorb a great loss, because there just isn’t time to make it again. Maybe the asset with the lower SD would be better for us.” Alternatively, his great granddaughter who is just starting to wear a little make-up might look at the same two assets and think, “He likes me better than any of the boys because I bring him his chewing tobacco and bleach the dribble-spots off his shirt. I’m gonna get his portfolio, and when I do, I’m going right for the highest return. With that kind of money, I’ll maybe marry a Prom King or something!”

Now that we have a comfort level with CAGR (“How fast does it grow?”) and SD (“How likely is that to happen?”), we’ll proceed next month to finding the CAGRs of various assets, and thence to Bonds.

This article is for informational purposes only and is not intended as professional advice. For specific circumstances, please contact an appropriately licensed professional. Klarise Yahya is a Commercial Mortgage Broker specializing in difficult-to-place mortgages for any kind of property. If you are thinking of refinancing or purchasing real estate Klarise Yahya can help. For a complimentary mortgage analysis, please call her at (818) 414-7830 or email [email protected].