# Post Modern Portfolio

The concept of Post Modern Portfolio Theory was developed over some shortcomings of the Modern Portfolio Theory. Like MPT, Post Modern Portfolio Theory also advises how the risky assets should be priced and how the rational investors can use diversification tools to optimize their portfolio returns.
It has been seen that under certain conditions the mean-variance analysis can produce unsatisfactory results. According to Markowitz, an economic model based on the semi-variance is more acceptable.

The two assumptions that make MPT produce unsatisfactory results are:
Investment returns of the portfolios and securities can be adequately presented by normal distribution
The variance of portfolio returns displays the correct measure of investment risk

In other way, it can also be stated that the result of MPT is limited by the measures of return and risk, which do not always stand for the realities of investment markets. The new risk-return paradigm thus established is known as the Post-Modern Portfolio Theory.

The present mathematical algorithms of Post Modern Portfolio Theory (PMPT) were developed by the Pension Research Institute at San Francisco State University in 1987. These methods offer a structure that helps to recognize the preferences of the investors for upside volatility over downside volatility.

The three-parameter lognormal distribution model for the pattern of investment returns was also introduced.

The downside risk in the PMPT model is given by the following equation:

d = 87308747 (t-r)2 f (r) dr, where the integration ranges from -8734; to t.

Here,
d = downside risk or downside deviation
t = minimum acceptable return or annual target return
r = random variable that represents the return for f(r), the distribution of annual returns
f(r) = lognormal distribution (three-parameter)

The Sortino ratio in PMPT model calculates the returns adjusted for target and downside risk.
Sortino ratio = (r-t)/d

Here, r is the annualized rate of return, d is the downside risk and t is the target return.