## MPF Evaluation

The math behind our optimal portfolio and analysis tool is based on Nobel laureate Harry Markowitz’s Modern Portfolio Theory introduced in 1952, which is the theory on how investors can construct portfolios to optimise or maximise expected return based on a given level of market risk. Since then, this model has been the cornerstone in financial modelling. According to the theory, it’s possible to construct a portfolio which offers the maximum possible expected return for a given level of risk.

The math behind our optimal portfolio and analysis tool is based on Nobel laureate Harry Markowitz's Modern Portfolio Theory introduced in 1952.

## How do you construct this portfolio?

One assumption in investing is that there is a relationship between return and risk.
High potential return is correlated to higher risk while low potential returns are correlated to lower risk.

According to Markowitz’s theory,
there is an optimal portfolio that could be designed with a perfect balance between expected return and risk.

## How to calculate returns?

The expected return of the portfolio is calculated as a weighted sum of the individual assets’ returns.
For JujuFund, we use historical data provided by Morningstar (a highly reputable data provider)
to input the expected return into our model.

For example, if a portfolio contained four equally-weighted assets with expected returns of 4%, 6%, 10% and 14%, the portfolio’s expected return would be:

(4% x 25%) + (6% x 25%) + (10% x 25%) + (14% x 25%) = 8.5%

## How to calculate risk?

The portfolio’s risk is a complicated function of the variances (also known as volatility, which is an industry standard measure) of each asset and the correlations (relationship) of each pair of assets.

To calculate the risk of a four-asset portfolio, an investor needs each of the four assets’ variances and correlation values between every combination possible. Because of the asset correlations, the total portfolio risk, or standard deviation, is lower than what would be calculated by a weighted sum.

## What happens when you combine all the possibilities of return and risks?

When you combine these two variables of expected return and risk,
every possible combination of assets that exists can be plotted on a graph,
with the portfolio’s risk on the X-Axis and the expected return on the Y-Axis.

The optimal portfolio does not simply include securities with the highest potential returns or low-risk securities.
The optimal portfolio aims to balance securities with the lowest degree of risk for a given level of potential return.
The points on the plot of risk vs. expected returns where optimal portfolios lie is known as the efficient frontier.