Harry W. Markowitz, the father of “Modern Portfolio theory”, developed the mean-variance analysis, which focuses on creating portfolios of assets that minimizes the variance of returns i.e. risk, given a level of desired return, or maximizes the returns given a level of risk tolerance. This theory aids the process of portfolio construction by providing a quantitative take on it. It integrates the field of quantitative analysis with portfolio management. Mean variance analysis has found wide applications both inside and outside financial economics. However it is based on certain assumptions which do not hold good in practice. Hence there have been certain revisions to it, so as to make it a more useful tool in portfolio management. Mean Variance Analysis2.1 Market assumptions The mean and variance analysis we do here uses many simplifying assumptions and approximations. A complete list would degenerate into philosophy, so here are just a few.
The matrix and the vector are known exactly.
The investor can purchase any amount of any asset, either positive or negative. Having a negative amount of a risky asset is short selling, or simply shorting. Having a negative amount of the risk free asset is called borrowing. There is no restriction that the number of shares owned should be an integer.
The investor is a price taker, which means that the investor may purchase any amount of the asset, and nothing the investor does will eect the asset price. The price per share is independent of the amount purchased. The price is the same for long and short positions. This really is a combi- nation of previous points.
There are no transaction costs, which means that if an investor rst buys w worth of any asset then immediately sells it back, the net change of wealth of the investor is zero. If there were transaction costs, this round trip would have a non-zero net cost to the investor. This also is implicit in the above points.
None of these is exactly true...
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