Asset Allocation

Report – Topic 3

Kristian Wiik Johnsen – s144189

The motivation for this topic, portfolio optimization, is to pick the right stocks/indexes to put in your portfolio. The reason why you want to do this is that you want an efficient portfolio. An efficient portfolio is a portfolio that rewards you the most in terms of expected returns versus the risk you have to take, also known as maximizing the Sharpe ratio. Furthermore, the motivation for today’s topic is being able to do a covariance matrix, and knowing how to compute the optimal portfolio with and without a risk free asset, and allowing and not allowing for short sale.

The method applied in this topic is in theory basic finance. The tricky part is to learn the excel formulas to compute the covariance matrix, variance, expected return and so on. The formula MMULT is in particular handy for multiplying several things at once, or to multiply matrixes so you don’t have to multiply one thing with another and so on. We started with computing the simple returns before be computed the mean returns for each market. Because of the bias in the mean computed from the simple returns, this number cannot be negative, we got a set of means for each market as well. The next step was to compute the covariance matrix. Then we could find the weights for each market in the portfolio. This was done by using the problem solver. The target cell was the variance cell, which was set to be minimized by changing the weight cells. The constraints added in the problem solver was in example that the sum of all the weights equals 1, when short selling’s not allowed the weight cells must be equal or bigger than 1. The constraints were changed depending on whether short selling was allowed and if there was a risk free asset or not.

The result we got from the NO RFA – SS allowed was to invest 100% in portfolio 1, which consists of UK(66.8%), Germany(-4.9%), France(27.9%), Italy(-32.7%), Netherland(-11.2%), Switzerland(78.3%) and...