The cardinal rule of investing: Never accept more risk than is necessary to obtain your investment goal. This is the underlying premise of Modern Portfolio Theory (MPT).

When give a choice of two portfolios with a projected return of 9.5%, one with a risk factor of +/- 12% and one with a risk factor of +/- 25%, a prudent man will always choose the portfolio with the +/- 12% risk factor. Likewise, given a choice of a probable return of 12% and a risk factor of plus or minus 50% or a probable return of 11% with the same risk factor, the smart money will always go for the 12 points. To do otherwise is gambling, not investing! Unfortunately, far too many American's are unknowingly gambling when they should be investing. Modern Portfolio Theory provides an answer for those individuals willing to commit the time to understanding its complexities.

Modern Portfolio Theory attempts to quantify the potential risk and the probable return of various portfolios of stocks and bonds and to provide a decision framework so that only the most efficient portfolios (those with the highest return for the lowest risk) are ever selected as investments. With the help of modern computers, the techniques of asset allocation can produce a virtually unlimited number of possible portfolios. Each with a different expected return (its average) and a different risk (uncertainty factor), as measured by the standard deviation of the portfolio's expected return. Some of these computer produced portfolios would represent the very best that could theoretically exist. (Those that provide the lowest risk for a given rate of return). Others would be marginal mixes of assets that have far too much risk for the return they are expected to provide. If plot these computer assembled, what if, portfolios on a graph, with the return going up on the Y-axis and the risk as measured by the standard deviation increase to the right on the X-axis, a interesting pattern begins to emerge.

The diagram above shows a number of portfolios, each with a different asset allocation. Each of the points on the graph above represents a different mix of asset allocations and each has a distinct pair of average return and standard deviation values. It is immediately apparent that not all portfolios are created equal in the risk return department. Some of the portfolios have both low return and high risk. A combination which should, of course, be avoided. Others start to stand out as the best of the bunch with the lowest risk for a given level of expected return. These top performers are beginning to form a curve at the upper limits of the data. This can be seen more clearly in the graph below.

On the above graph we have plotted all the portfolios that have the same rate of return on the horizontal line and all the portfolios that have the same risk (standard deviation) on the vertical line. We will consider the horizontal line first. The points along this line all have the same predicted return (average), but each of the portfolios has a different risk. The far right one goes on the line, the higher the risk. This line clearly demonstrates that some asset allocations minimize risk, while other asset mixes expose the portfolio to a great deal of risk. Given a choice of two or more portfolios with the same return, the smart investor will always choose the one with the lowest risk. Therefore, the farthest left point on the line is the most efficient. The point at which asset allocations are optimized. Modern portfolio theory tags this the most efficient portfolio, because it is the one that produces a given rate of return at the lowest level of risk. Also notice that the right end of the horizontal line could go on for quite a ways, because in the investment markets there are tons of ways to make risky choices. Note that the left side of the line ends before it reaches the Y-axis (Return). This is because there are no portfolios that provide this amount of expected return, without accepting some level of risk. The far left end of horizontal line is the best portfolio we can construct from using any possible mix of assets.

Now let’s focus on the vertical line. The vertical line represents all portfolios with the same amount of risk. Portfolios near the bottom of the line are not very efficient, because they accept the same level of risk at which other portfolios provide a higher return. At the top end of the line is the most efficient portfolio. It provides the highest projected return for a given level of risk. No intelligent investor would accept a portfolio with the same level of risk that pays less than the highest return. That is gambling, not investing.

The Efficient Frontier

In the graph above we went ahead and filled in all the possible portfolios for various rates of return and risk levels. This creates a line, called the ‘efficient frontier’. (see above). The efficient frontier is comprised of the left end points of the horizontal rate of return lines for each rate of return. Similarly, the efficient frontier is represents the top of the vertical stand deviation line for each incremental change in the level of risk.

All the optimal portfolios are on the efficient frontier line. Any portfolio below the line either has more risk that it’s more efficient alternative or provides a higher return for the same level of risk. The wise investor will only purchase portfolios that are on the efficient frontier line. Every point below the line represents an allocation of assets that are more risky than their efficient alternative. In other words, all the portfolios that are not on the line are sucker bets. There are no portfolios above the line, because based on historical data, those portfolios do not exist.
To complete Modern Portfolio Theory, we need to add one last nuance. Please note that if one follows the efficient frontier line down and to the left, the portfolios provide lower and lower returns at lower and lower risks levels. However, there is a point where the allocation of assets provides a return that is below the return that is available from US Government T-Bills, which do not have market risk. Remember, that asset allocation is designed to minimize systemic or market risk. If there are places to put your cash, that earn interest and do not have market risk, then we no longer need asset allocation.

In Modern Portfolio Theory, federal t-bills are assumed to be the zero risk alternative to the market. In actuality, t-bills also fluctuate in the market with the general level of interest rates. However, since they are of such short duration (90 days) and are backed by the federal treasury, they can be considered essentially, risk free.

It is interesting to note that the graph shows mixtures of assets that will produce a return equal to, or lower than, that available from T-bills. However, these entail the acceptance of market risk. Our original premise was to minimize risk, so why would we ever accept market risk, when we can get the same return risk free? Prudent investors will not do so. Therefore, an investor, using the dictates of Modern Portfolio Theory, will select his or her portfolios either from t-bills or the efficient frontier line but switch to t-bill is the desired return is equal or lower. In actuality, a portion of the portfolio may be held in t-bills, which may lower the risk of the overall portfolio. T-bills are in effect included in the choice of allocatable assets.

Savings Alternatives

Also in actual practice there are a number of substitutes for t-bills. Those most frequently used are various savings outlets such as Bank and credit union CD’s or annuity deposits with an insurance company. These have historically provided slightly higher returns than t-bills. It is of course up the individual to judge the risk difference between a t-bill and a CD or an insurance annuity deposit. T-bills are a direct obligation of the U.S. government. CD’s have limited backing through a federal agency and insurance deposits limited guarantees from state emergency funds. (see ???)

Recently, indexed annuities have introduced a new element of sophistication and complexity into MPT. The indexed account carriers a minimum interest guarantee and an expected return can be calculated. However, unlike all the other assets that are allocated in an MPT portfolio, an indexed account has no market risk. The principal and the minimum interest rate are guaranteed. The only uncertainty in an indexed account is how much, if any, bonus interest will be paid in addition to the minimum interest that is guaranteed. How an indexed account fits into MPT is still a matter of substantial debate among financial experts. However, the entire thrust of MPT is to minimize risk. Indexed accounts are a method of doing just that. (see Zero Market Risk)

Note: The methods discussed herein, were developed to deal with uncertainty. When you invest in the stock market or the bond market, no one knows the outcome. On year after making your investment you might be treating yourself to an expensive vacation. You could also be mourning the loss of your funds and vowing never to venture into the stock market again. Markets are uncertain and we use uncertain tools to help us mitigate the risk. Modern risk management techniques plan according to what is probable, with an implied hope that we will be spared the worst of what is possible.

It is vital to understand that the level of risk level is measured statistically and based on historical relationship developed under prior economic conditions. There is no guarantee that future movements of the sectors within a given portfolio will behave as expected. Asset allocation lowers the possibility of risk; it does not eliminate it. New economic conditions or a national emergency could temporarily or permanently undermine the historical price relationship between market sectors and render your portfolio high risk.