“The Theory of Everything” – A Discussion of the Time Value of Money

June 28th, 2018 | posted in: Investing

by: William Spitz

The Theory of Everything

This enjoyable movie chronicles the work of the late physicist Stephen Hawking in his quest for a unified theory of the universe.  He was searching for a single theory that would at the same time explain the movement of sub-atomic particles on the one hand, and the behavior of stars and galaxies on the other.  In fact, there are two theories, general relativity and quantum theory that seem to explain many cosmic phenomena. But, physicists tell us these two theories are mutually exclusive, they cannot both be right.  So, the search goes on.

Fortunately, in finance, we have something close to the theory of everything and that is the time value of money, otherwise known as compound interest.  The concept and calculation of present and future value are the first things you learn in Finance 100, but it turns out they are the basis of a great deal of investment analysis.  While there are certainly many methods of making investment decisions and lots of fancy math and computer algorithms, the time value of money and its offshoot, valuation, are at the heart of the entire field.  And, the same basic techniques are used by corporations making capital expenditure decisions and investors in stocks, bonds, real estate, private equity, and so on.  At Diversified Trust, our investment decisions are based on many variables including economics, demographics, politics, world affairs, and market forces.  But, central to our analysis is the valuation of various asset classes and the resulting projected return on them. So, while you probably aren’t interested in a deep dive on this rather technical topic, a brief tutorial will give you some insight into the thinking that drives our asset allocation decisions.

The Basics

The starting point of all finance is the principle that the value of any asset is equal to the present value of the future cash flows that will be received by virtue of owning that asset.  Making this calculation involves two basic steps: forecasting the cash flows that will be received, and discounting them at an interest rate that reflects the return that could be earned on other investments as well as the perceived risk or uncertainty in the forecast of those cash flows.  In the case of most bonds, the cash flows (interest payments and maturity value) are known, whereas they must be predicted for most other types of assets.  For example, in the case of real estate, the future cash flows consist of the annual net income on the property and an assumed future sales price, neither of which can be predicted with certainty.

Actually, there are two basic approaches to this calculation.  First, using forecasted cash flows and an appropriate discount rate, one can calculate a “fair” value which is then compared to the current price to determine whether the asset is cheap or expensive.  Alternatively, using the forecasted cash flows and actual current market price, you can solve for the discount rate which becomes the expected rate of return on the investment.  In order to give this number crunching  a sense of relevance, please note that the first method is one of three calculations (along with replacement cost and comparatives) generally used by an appraiser to estimate the fair value of a piece of real estate.  And, the second approach is used by corporations to calculate the internal rate of return on a potential investment in a new piece of equipment or plant which is then compared to other possible projects and the company’s cost of capital.

Stock Valuation

As previously mentioned, the same technique is frequently used to value either an individual stock or the stock market as a whole. This version of the discounted cash flow analysis is called the dividend discount model and entails forecasting future dividends which are the cash flows you receive as a shareholder.  Some people add bells and whistles of various kinds to these models, but we will stick with the basic version.  While useful and conceptually straightforward, this method is actually demanding because an analyst must forecast an infinite stream of dividends.  Or alternatively, one can forecast dividends for a specified period of time and then assume that the stock is sold which requires a decision as to how it will be valued at the time of sale.  Consider the difficulty in forecasting future dividends for companies such as Google or Berkshire Hathaway that do not currently pay a dividend.  When will they start and how rapidly will the dividend grow?

For companies that do currently pay a dividend and are growing at a stable rate there is a shortcut that requires only three inputs: the current dividend (which is known), an assumed growth rate in dividends, and the discount rate. And this calculation can actually be simplified into the well-known and widely used price/earnings or P/ E ratio.  So, when market commentators suggest that the U.S. stock market should be selling at a P/E of say 23, they are actually making an implicit assumption about its future growth rate and appropriate discount rate.  In other words, the P/E is just a greatly simplified discounted cash flow model.

Other Assets

Interestingly, the same shortcuts are used in many other asset classes. Real estate investors discuss the “cap rate” for an asset which is just the reciprocal of the P/E.  So, a property selling at a P/E of 20 would have a 5% cap rate.  Private equity investors focus on the price/ebitda ratio where ebitda is earnings before interest, taxes, depreciation, and amortization.  And, bond traders quote the yield to maturity which is just the discount rate or return that equates the current price of the bond to the present value of future cash flows. You needn’t understand the ins and outs of all of this; the point is that these are all basically the same thing- in other words, the theory of everything.

Valuation in Practice

Let’s consider the use of these tools in evaluating both individual stocks and the stock market as a whole. Most equity managers use one form or another of these models to calculate either the fair value or projected return on each stock in their universe and these metrics are then used to rank stocks in order of their relative attractiveness.  For quantitative managers, this analysis is often a major if not primary input to their actual investment decision whereas more qualitative managers use it as a screen to identify stocks for further traditional security analysis which includes interviewing management, evaluating products and competitors, and so on.  At Diversified Trust, we don’t actually select stocks, so let’s turn to the evaluation of asset classes such as large capitalization U.S. stocks, emerging market equities, and other categories.

While it is very difficult to accurately forecast future dividends for a given company, long term earnings and dividend growth rates for an overall category such as the S&P 500 are much more stable and predictable.  The following chart depicts annualized historical 10 year dividend growth rates for the S&P 500 and you will note that the fluctuations are within reasonable ranges.  So, in the absence of a major change in the world, we should be able to forecast future growth rates within a tolerable margin of error.

S&P 500

We will use the version of the model that assumes a sale of the index at the end of ten years so the next step is to forecast a P/E ratio in year 10 which is then multiplied by future earnings to estimate a future sales price. Typically, practitioners assume that the P/E will regress from its current level to the long term average over the ten year time frame. Then, the present value of annual dividends and the future sales price is compared to the current price to calculate an annualized rate of return. We then combine this expected rate of return with a number of other inputs such as forecasts from other respected investment firms and a model that imputes projected returns from the relationship between different asset classes.  The net result of all of this is our forecast of the expected return and risk over the next 7 to 10 years for a variety of asset classes.  Finally, using these inputs, computer optimization models, and a dose of judgement, we construct recommended portfolios.  I am sure you are bored to tears by these details, but the important message is that constructing portfolios is a blend of art and a good deal of science.

The Illusion of Precision

Given all of this math, why aren’t forecasts of stock market behavior more accurate? Basically, there are two ways one can err.  First, the forecast of future dividends can be off the mark, although the previous section indicated that the likely error should not be terribly grievous.  The more important source of error is the forecast of the future P/E ratio.  As previously mentioned, the discount rate and/or P/E are a function of returns on other potential investments and the perceived risk associated with the particular investment under consideration.  As a proxy for other investments, most people use the yield on something like the 10 year U.S. Treasury bond which is obviously a known quantity.  So, the big unknown is the appropriate risk premium.  In other words, how much extra return should one demand for this particular investment versus a safe U.S. Treasury?  Interestingly, this risk premium is basically a measure of investor sentiment and therefore fluctuates significantly over time with the rise and fall of investor emotions.  It is difficult to know exactly what risk premium is priced into the market at any given time, but a rough guess is that it has historically fluctuated between negative 3% and positive 13% with an average of about 4.0%.  That is a massive spread, and I find it very difficult to conjure up a reason why it should ever be negative.  To place this uncertainty in perspective, holding everything else constant, a 1% change in the assumed risk premium changes the fair value by about 30%!

One other interesting tidbit is that the impact on valuation of changes in things like government policy is very hard to predict. For example, using the dividend discount model, a corporate tax cut would likely increase future earnings and dividends (the numerator).  But, if this cut is expected to increase the US budget deficit, it might lead to an increase in interest rates. (The denominator)  The two effects tug valuations in the opposite direction so the net effect is unclear.

Despite these issues, valuation does provide important information about potential returns as illustrated by the following chart:

This chart covers the period 1871-2018 and shows the subsequent ten year annualized return given the starting P/E. Please note that the line slopes downward to the right which means that a higher beginning valuation as measured by P/E results in a lower subsequent return, just as you would expect. And the pattern is fairly tight which means that the predictive value is good. But, it is important to point out that while the predictive value is strong for a ten year time frame, valuation has little or no forecasting ability over short time periods which tend to be dominated by momentum factors.

Art and Science

This post is probably overly technical and includes more information than you ever wanted on valuation, but we think it is very important for our clients and friends to understand our investment process.  Putting aside all of the details, the following are the key takeaways:

  • There are widely accepted and time tested methods of forecasting returns on various asset classes.
  • While we work very hard at refining the inputs to the process, you should understand that they vary considerably over time rendering the forecasts subject to error.
  • These forecasts do actually have pretty good predictive value over 7-12 year time horizons but provide little or no insight into near term returns.
  • We combine these forecasts with a number of other inputs to formulate both short and long term recommended portfolio structures using a blend of both technology and judgement.
  • While the entire process is imperfect, it is greatly superior to a “seat of the pants” approach to building portfolios which is often unduly influenced by recent market behavior and emotions.

One final comment; because of our belief in this discipline, we typically avoid investments such as gold, art, and Bitcoin which are exceedingly difficult to value because they do not generate cash flows.   The absence of cash flows means that the only source of return is the assumption that some other investor will buy from you at a higher price. That may well occur, but these types of investments don’t fit our analytical framework, and one lesson that we have learned is that successful investors are disciplined about sticking to their process.