Sunday, April 4, 2010

Time, Inflation, and Uncertainty

This article discusses a little of the theory behind why investors expect to make money on investments, and why they expect to make more money on some investments than others.  This post is a bit more theoretical than most so far.

Investors give up the use of their money for a period of time with the expectation that they will receive more money in the future.  The additional amount of money received in the future is known as the return on the investment.  Return usually is expressed as an annual rate of return.  If you invest $100 and receive $105 one year later, your rate of return is 5% (see note 1).  Rate of return often is referred to simply as return.  The average (mean) of the probable returns on an investment is known as expected return.  For example, if there's a 50% chance that an investment will return 5% and a 50% chance that it will return 7%, the expected return is 6% [ (5% + 7%) / 2 ].

In giving up the use of their money for a period of time, investors expect to be compensated for three things:
  • Time: Waiting until some future time to spend their money (deferring current consumption)
  • Inflation: The expectation that things they spend their money on  in the future will be more expensive
  • Uncertainty: The possibility that they won't make as much money on their investments as expected, or even that they will lose money

People seem to prefer spending money on goods and services now rather than later.  So, when someone defers current consumption (waits to spend their money on goods and services), and lends or invests the money, they generally expect to be paid back more money in the future.  Even if goods and services cost the same in the future as they do now, people generally still want to be compensated for giving up the use of their money for a period of time.  The longer you must wait to get your money back, the more you expect to get back.  This is known as the time value of money.


If people expect things to cost more in the future, they generally expect additional compensation for deferring current consumption.  In addition to being paid to wait to spend their money, they also expect to be paid enough so that they can buy the same amount of goods and services in the future as they can in the present.  Therefore, they expect additional payment to compensate for the expected rate of inflation.

Rational investors expect all investments to compensate them for time and expected inflation.  The current inflation and time value of money components of return can be determined by observing the interest rates on savings accounts, money markets, and short term government securities (T-bills for US investors).  Since investors aren't locked into these short term investments (i.e, they can switch investments easily at no cost), short term rates tend to adjust rapidly to changes in perceived inflation and to changes in the time value of money.

Although we don't know what inflation will be in the future, we can compare two different types of bonds to determine what investors are anticipating it to be over certain time period.  The two types of bonds are US Treasury Inflation-Protected Securities (TIPS) and US Treasury bonds (see note 2).

TIPS pay a stated interest rate on inflation adjusted principal.  For example, if you buy $100 worth of 2% TIPS, and there's 2% inflation during the following year, you will be paid 2% of $102 or $2.04 in interest (see note 3).  Also, when your TIPS mature (are paid off), you will receive the inflation adjusted principal (or the original investment if inflation has been negative).  Using our current example, if you sold your TIPS after 1 year, you would receive $102.  Your total rate of return would be slightly over 4%: $2 in capital gain due to inflation and $2.04 in interest.  Of your return, 2% compensated you for time, and 2% compensated you for inflation.
By contrast, Treasury bonds pay nominal interest only -- there is no inflation protection.  If you buy $100 of a 4% Treasury bond, you will receive $4 in interest each year, and you will be repaid your $100 original investment when the bond matures.  If inflation averaged 2% over the life of your treasury bond, your real (after inflation) return would be about 2%, or about the same as the TIPS in the previous example.  Since Treasury bonds don't provide guaranteed inflation protection, the compensation for expected inflation contributes to the interest rate demanded by investors.

The difference between TIPS and Treasury Bond yields (another word for interest) of a similar maturity (e.g., 5 years, 10 years, etc.) tells us what investors are expecting inflation to be over that period of time. So, if a 10 year TIPS currently is yielding 2% and a 10 year Treasury Bond is yielding 4%, that implies that investors currently expect inflation to average about 2% over the next 10 years.  Of course this is just the expectation, which could turn out to be very wrong.

With the Treasury Bond in our example, you are being paid 2% for the time value of your money, and 2% for expected inflation.  With the TIPS, you are being paid 2% for the time value of your money, and you are paid for actual inflation (as opposed to expected inflation).  With either of these investments, there is virtually no uncertainty that your principal will be repaid, and that you'll receive your nominal interest payments (there is uncertainty in the inflation adjusted component of the interest on TIPS).


If there is uncertainty that the payments received in the future will adequately compensate investors for time and inflation, then it's rational to expect additional compensation for this uncertainty.  For example, most people would prefer a guaranteed return of 10% rather than a 50/50 chance of either a 15% or 5% return (even though the expected return of both investments is 10%).  However, people are more likely to be tempted by a 50/50 chance of an 8% or 15% return, since although there is some uncertainty, the expected return is higher than 10% (the expected return is (8% + 15%) / 2 = 11.5%).

In investing, uncertainty is the most commonly used indicator of risk. An investment with higher uncertainty of return is considered a riskier investment.  Statistical methods are used to estimate the uncertainty (risk) of investments, and standard deviation is the most common measure of risk.  Standard deviation is a measure of how scattered the returns are around the average (mean) return.  We won't get into much technical depth here, but let's look at a few examples to get an intuitive feel for the uncertainty and standard deviation of returns.

First, assume we invest $100 in an FDIC insured Certificate of Deposit (CD) with a term of 5 years paying 3% annually.  We are virtually guaranteed that we won't lose our original investment, and unless the bank issuing the CD goes out of business, we are guaranteed to get $3 in interest each year (if the bank goes out of business, we'll get our $100 back, but will have to find somewhere else to invest it).  The average (mean) return is 3%, and the standard deviation is 0%, since there is no variation in the annual returns.  Here we are considering only nominal returns (i.e., not considering inflation).

Next assume we invest in a bond fund that pays the following rates of return for 5 years: 4%, 3%, 4%, 5%, 4%.  The mean return is 4% (add the annual returns and divide by the number of years, 5), but the returns vary from year to year, so the standard deviation is greater than zero (it's 0.6%) (see note 4), and this is a riskier investment than the CD.

Finally, consider a stock fund that has the following annual returns for 5 years: 4%, -8%, 16%, 6%, 2%.  The mean return is 4% (the same as for our bond fund), but the standard deviation is 7.7%, and this would be considered a much riskier investment than the bond fund or the CD.

Although we don't know what the future returns will be, the historical performance of various investments gives us some idea about what the uncertainty in the future returns might be.  Investors typically look at past returns to evaluate the uncertainty of future returns.  From the examples above, assuming the returns in future are somewhat similar to those in the past, we can see that a higher standard deviation indicates that the return in any one year is more likely to be further away from the average return -- either above or below it.

Risk Premium

Investors demand higher expected returns for riskier investments.  The additional expected return compared to a risk-free investment is known as the risk premium.  Treasury bills (T-bills) are commonly considered the risk free investment to which other investments are compared (T-bills are short term US Government securities, maturing in 1 year or less).  For most individual investors, FDIC insured savings accounts or short-term FDIC insured CDs can be considered the risk-free investment.

It's extremely important to understand that higher expected returns require taking more risk.  Remember that we're defining risk as uncertainty in the rate of return.  So,  to increase the probability of higher returns, you must live with the possibility of lower returns.  If you are unwilling to live with higher uncertainty of returns, you must accept the certainty of low returns.  The higher the uncertainty of an investment's returns, the higher the risk premium investors will demand.

High quality short term bonds and bond funds have a fairly small risk premium.  They generally have somewhat higher yields than risk free investments.  High quality intermediate term bonds and bond funds usually have higher risk premiums, and thus higher yields than short term bonds and bond funds.  In general, the longer the term to maturity and the lower the quality of a bond or bond fund, the higher the risk premium and yield (occasionally longer maturity bonds will have lower yields than shorter maturity bonds; this is known as an inverted yield curve).

Stocks and stock funds are generally riskier than bonds, and therefore the market tends to price stocks so that they have a higher expected return than bonds; i.e., they have a higher risk premium.


Investors expect to be compensated for giving up the use of their money for a period of time, for expected inflation, and for any uncertainty of returns.  The expected returns of various investments are compared to the risk free rate of return.  The risk free rate of return is basically the interest you can get on a T-bill, an FDIC insured savings account, or a short-term FDIC insured CD.  The more uncertain the returns of an investment, the higher the expected return.  The expected return above and beyond the risk free rate is the risk premium.  You must take more risk to have the probability (but not certainty) of higher returns.


1 In trying to keep this simple, I'm avoiding all but the simplest mathematical expressions.  The purpose here is just to give you a general idea about what terms such as return and expected return mean.

 2 Bonds are one type of US Government Treasury securities.  The other types are Bills and Notes (and of course TIPS).  Bills are short term, maturing in 1 year or less.  Notes are intermediate term, maturing in 1-10 years, and bonds are long term, maturing in more than 10 years.  In the article, I use the generic term bonds to keep things simple.

3 More acurately, every 6 months the inflation adjusted value of TIPS are recomputed, and interest is paid.  To keep the example simple, I'm assuming annual payments instead of semi-annual payments.

4 To determine the standard deviation of the returns in these examples, I entered them into a Google Docs Spreadsheet, and used the standard deviation formula (STDDEVP).


  1. Very well written article... When investing, is it common to go all or nothing? For example, let's say someone was more comfortable with risk-free returns. Do people generally make all these types of investments, or is it typical to invest in some investments with risk-free returns while also investing in others with more risk?
    Furthermore, I'm curious how one might analyze past returns to look at the uncertainty of future returns. This may be the more technical, in-depth stuff you are trying to avoid, but I'm curious if it's understandable by someone like me...hmmm, there's a challenge for you!!

  2. Portfolio theory suggests combining risky assets with risk free assets, based on your risk tolerance. So, if you have zero risk tolerance, you would invest only in risk-free assets. Most advisors recommend using a combination of risky and risk-free assets, or at least using low risk assets (like high quality short-term bond funds) to reduce the risk of your portfolio to a level that's appropriate for you.

    The examples in the post actually demonstrate how one might use past returns to estimate the uncertainty of future returns. You look at the variation (standard deviation) of past returns, and assume that the variation of future returns will be similar. So, stocks have had more variation of returns than bonds in the past, so most people assume stocks will have higher variation of returns in the future (i.e., that they will continue to be riskier than bonds).

    This actually is what usually is done, although it's good to keep in mind that the future may be different than the past.