The focal point in MPT is the mean or average return. The focal point in PMPT is the Desired Target Return needed to accomplish the investor’s financial goal. The DTR is the missing link between the investor’s assets and future cash outflows. I originally called this the minimal acceptable return or MAR. Attorneys convinced me to change it to DTR since MAR might be interpreted as a guarantee of what an investor would receive “AT MINIMUM.”

We do live in a litigious society here in the states.

MPT measures risk as dispersion either side of the mean. PMPT measures risk as dispersion below the DTR. Dispersion above the DTR is the reward for taking on the risk of falling below the DTR. MPT measures the risk of not achieving the mean as standard deviation. PMPT measures the risk of not achieving one’s investment goal as deviations below the DTR. The underlying theory for PMPT was developed by Peter Fishburn when he was at the University of Pennsylvania.

I would like to start off this blog with a note from my friend and colleague, Hal Forsey:

Some Thoughts about Optimization

From Utility Theory

a) If the outcome from a choice of action is known with certainty then the optimal choice of action is the one with outcome of greatest utility.

b) If the probability distribution of the outcomes from a choice of action is known then the optimal choice of action is the one with the greatest expected utility of its outcomes.

c) If the probability distribution of the outcomes from a choice of action is only approximate then the action with the greatest expected utility may or may not be a reasonable choice of action.

Utility Theory applied to choosing an optimal portfolio

a) If the return from each possible investment is known with certainty then the optimal investment portfolio is a 100% allocation to the investment with the greatest return. This only assumes that the utility function is an increasing function of return.

b) If the joint probability of returns for the set of possible investments is known and if the utility function for portfolios with a given variance increases as the expected return increases then the optimal portfolio in on the mean-variance efficient frontier.

c) If the joint probability of returns is only approximate then portfolios on the efficient frontier may or may not be reasonable choices.

Comments about mathematically optimal solutions and real world problems

Optimal solutions to a mathematical problem are often on the boundary of possible solutions. This causes problems in applying mathematics to real world situation as the mathematical model used to describe the situation is often only an approximation. So the mathematical solutions to the model will often be extreme and since the model is only approximate the solution to the model may be far from optimal.

Think of the case in which the returns of the possible investments are thought to be known with certainty. The optimal solution might be a portfolio of 100% in oil futures. This is fine if the outcomes are actually known with certainty, but is extremely risky if this assumption is incorrect.

Even when it is only assumed that the joint probability of returns is known, limiting solutions to some efficient frontier will give extreme portfolios that may be far from optimal if the probability model does not fit reality. For example many probability models have thin tails that may lead to underestimating probabilities of large losses. This may, for example, lead to portfolios with too much weight in equities.

So maybe, the best one can do is to use the mathematics as only a guide in selecting portfolios.