Continued from Part 3 . . . The Horse

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). 

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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 ‘cause 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!”

We have seen that lenders are increasingly requiring new borrowers to have, in reserve, liquid funds at least equal to 10% of the loan amount. These funds do not have to be in low yielding accounts. They do not have to be dead money. They can be invested in liquid assets. One common choice is to place reserve funds into a well chosen stock / bond portfolio.

This series of articles, intentionally named “Information, Not Advice”, is intended to explore some aspects of the stock / bond approach. It is expected that the interested investor will consult with an appropriately licensed professional before doing anything silly. 

We now dip our toe into the shallow end and begin to explore the CAGR (Compound Annual Growth Rate) which estimates “What am I going to get?”and the Standard Deviation (“How sure am I to get it?”) of common asset categories. 

There are lots of possible investments, but the big three are stocks, bonds, and income properties, informally referred to as Bourse, Bonds, and Buildings. This is Bourse Month. We’ll do Bonds and Buildings another time.


Because it reports after-inflation gains, our major data source is There are other sources of data, but many do not adjust for inflation. A stated return that does not include the effects of devalued money misstates the benefits of the investment. That can be significant. 

Pre-WWI inflation in the Weimar Republic is legendary. The value of the German mark cascaded downwards until, in November 1923, it took 4,210,500,000 marks to buy one US dollar. 

More recently, Zimbabwe’s rate of inflation in the early winter of 2008 was 79,600,000,000% month-on-month. Earlier this year (2019), Venezuela’s inflation was reported at 905%. These are not insignificant figures.

Right now Iranian banks offer 18% interest on deposits (payable in Iranian rials) while the official rate of inflation is 52%. So, pretty, young Afsaneh, who wants very much to one day to have her own business, decided to begin saving for a small kabobery. She opened an account at the neighborhood bank and deposited 100 rials. At the time of her deposit, rice was one rial per pound. One hundred rials would buy 100 pounds of rice. It is now a year later and Afsaneh’s account has indeed grown to 118 rials including earned interest, but the price of a pound of rice has increased to 1.52 rials. Her 118 rials now will no longer buy 118 pounds of rice. It will not buy 100 pounds. It is enough for only 78 pounds of rice. Afsaneh, a bright young woman, quickly learned that inflation is a most insidious threat to wealth, even greater than high taxes. Maximum tax rates cap out at 100%, but inflation has no ceiling.

To resolve the inflation issue, Iran recently chopped four zeros off its currency. This follows Venezuela’s lopping of five zeros earlier this year. It’s not entirely clear how the removal of zeros will be helpful, because high inflation still means we’re talking about a barter economy. “You want $10,000,000 for that dog? I’ll trade you two $5,000,000 cats.”

Clearly, if one is going to forecast the anticipated results of an investment, using “real” return data (“real” meaning net of inflation) can be pretty important. 

CAGR (“What am I going to get?”)

Still referring to, the average (“mean”) inflation adjusted return for the total US stock market (TSM) since 1970 has been a real return of 7.6%, with a standard deviation of 17%. 

A real return of 7.6% over 25 years turns $10,000 into $62,000 (rounded).  That’s not too shabby: the original investment multiplied six times over 25 years in inflation adjusted dollars. 

Numbers like these, which are unleveraged, should impress even the jaded apartment investor. They compare favorably with what’s happened to single family homes in Los Angeles County over the past 25 years. We can make this comparison because well located real estate tends to adjust to inflation automatically, so in both cases we are using inflation-adjusted (ie, “real”) numbers. In 1993 the average sales price of a SFR in Los Angeles County was $195,500. In 2018 the figure was $615,000. That’s a CAGR of 4.70%. Both SFRs and the Total Stock Market (TSM) gained during the last 25 year period, but the Total Stock Market grew at 7.60% and the SFR market grew only 4.70% annually.

The stock market grew 62% more than the famous southern California housing market. Who would have thought?

There’s more to this story, including matters we haven’t touched on, but that should be considered. These include (but are not limited to):

  • Benefits of leverage (advantage: real estate).
  • Benefits of liquidity (advantage: stocks, bonds).
  • Management (advantage: stocks / bonds).
  • Real Estate:  the purpose of well-located real estate is to provide both capital gains when sold and cash flow from month to month. 
  • Stocks:  the purpose of stocks in a portfolio is to provide capital gains. The dividends are nice, but are probably better reinvested.
  • Bonds:  the purpose of bonds is to protect the stocks. History shows that a “low” stock market will recover in time. The loss is temporary, even if it takes a generation to recover. If an investor sells her stocks simply because the market is down, she’s turned a temporary paper loss into a permanent loss of capital. But bonds are like teen-aged boyfriends: they are easily substituted. Sometimes it only takes a mother’s talk and a cup of hot chocolate.
  • And, no matter what, past performance is no guarantee of future results. As an obvious example, we know that interest rates peaked in Sept 1981 (10 year note @ 15.32%) and subsequently declined over next 30+ years to 2.07%. That gave asset values a massive boost (“As rates go down, values go up”) that we are not likely to see repeated.

Takeaway 1:  Stocks can provide a higher return than unleveraged buildings, but are more volatile.

Takeaway 2:  Bonds act as the keel of a sailboat: the boat can still rock back and forth, sometimes violently, but a keel reduces the chance of capsize.        

Standard Deviation (“How sure am I to get it?”)

The standard deviation (SD) straddles the mean (the “average”), with half the SD on one side and the remaining half on the opposite side.

The SD for the Total Stock Market (per is 17%. That is, the range containing two-thirds (rounded) of the investors likely return runs from 17% beneath the mean to 17% above it: in this case, from minus 9.4% (7.6% less 17%) to positive 24.6% (7.6% plus 17%).

In some years the market rose (or fell) more than one standard deviation. In 1995 the market increased 33.5%; in 2013 the increase was 26.5%. There were also big downside years that exceeded one SD. In 2008 the market fell 33.8%. 

So gains and losses can exceed one standard deviation, but 2/3rds of the time yields cluster on both sides of the mean (the “average”). The SD expresses the investment’s risk.

As we’ve seen, not many people can accurately forecast what the market is going to do over the short term. Historically, however, the real return of the stock market has been 7.6% per year over the long term.

Takeaway 1:  Stocks are volatile. People that make short term investments in volatile markets are called speculators, and few experience much success. Stocks are more appropriate for the long term investor, the investor that can wade through inevitable market declines (sometimes very serious declines) without losing her composure and turning a temporary market decline into a permanent loss of capital.

Takeaway 2:  On the other hand, there is historical data suggesting that the unleveraged real return on stocks might be at least comparable to income properties. Many people find that surprising.

Make a Different Investment, Get a Different Return

For the purposes of this article, the wise investor is defined as (a) one who knows how to recognize sound individual stocks, or failing that, (b) one who just gives up and buys the market (possibly through a low cost ETF). Either extreme on the investor’s radius of competence will do. The saying is, “If you can recognize good individual investments, buy them. If you can’t, buy the market (the entire market or market sector) and piggy-back on market’s organic gains.” 

Example:  An example of a specialized sub-market would be the small cap “value” tranche. Data shows that over time small caps can yield a lot more than large established companies, however, small caps are much more volatile. But they can still be a useful portfolio addition at times.

For example, the stock investor doesn’t have to invest solely in TSM if she’ll accept a higher standard deviation (i.e., a greater risk). She could buy more narrowly focused investments. For example, the investor could put 2/3rds of investable funds into LCV and 1/3 into Small Cap Value. 

Using historical data, how might that turn out? Just to review, we’ve already seen that an investment in the Total Stock Market returned a 7.6% CAGR over the past 25 years ($10,000 became $62,000). During that same 25 years an original investment of $10,000 in Small Cap Value companies, which indicates compounded at 11.4%, grew to $148,000. That’s not the 6-fold return of the TSM, it’s nearly a 15-fold return. But, of course, Small Cap Value stocks are riskier (SD 19.7%).

Our hypothetical investor wants an above-market return at the lowest risk she can get away with. There might be several options. Below is one alternative. 

What if the investor puts only 2/3rds of her stock funds into a Total Stock Market fund (total return estimated at 7.6%) and 1/3rd into a Small Cap Value fund (total return estimated @ 11.4%). In that way the majority of her stock portfolio would be in larger companies with a smaller SD (and thus safer), and a smaller portion would be in more volatile (riskier) “higher return” companies. The numbers might look something like this:

Total Stock Market Stocks @ 7.6% CAGR / SD 17%

Small Cap Value Stocks  @ 11.4% CAGR / SD 19.7% 




This is why an investor in stocks / bonds should have a competent professional advisor. There are some good advisors that have had no formal education, but many have earned the CFP or CFA designations. Next month … Bonds. The blended portfolio compares very favorably, in both CAGR and SD, with the return from the TSM (only) investment we saw in the above. The return is a full 130 basis points higher (8.9% minus 7.6%). The SD is only 90 basis points higher. Yet the initial principal grows 36% more. Sometimes taking a little greater risk is worth it.


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].