All of the models to be discussed, i.e. Markowitz, Single Index, CAPM, and APT, have one single goal that is accomplished by using them. This goal is to make a portfolio, or individual securities, as efficient and well performing as possible by finding the optimal weights, highest return, and lowest risk.
The Harry Markowitz model of 1952, or the mean-variance model, was one of the earliest models created to compare and contrast securities outcomes. This model uses the weights, standard deviation, and covariance for each security, creating a weighted covariance matrix, therefore forecasting a very accurate estimate of what return and risk the securities or portfolio would give.
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There are a handful of assumptions associated with the Markowitz model. The first is that the risk of a portfolio is based on the variability of returns from said portfolio. Second, that an investor is risk averse. Third, the investor prefers to increase return. Fourth, and due to numbers two and three, is that the investors utility curve is concave and increasing. Fifth is that an investor either maximizes his return for a given level of risk or maximizes his return for the minimum risk. Finally, number six, which is that the investor is rational.
As for the Single-Index model, the main assumption, in order to simplify analysis, is that there is only one factor that causes the systematic risk that affects all stock returns, which can be represented by the rate of return on a market index. This model is probably the least restrictive of them all.
The CAPM model, though more similar in process to the Single-Index model, actually has much more restrictions, posing similarities towards the Markowitz model. The first is that security markets are perfectly competitive (small, price-taking investors). Secondly, markets are frictionless with no taxes or transaction costs. Thirdly, investors have only one and the same holding period. Fourth, there is only perfect information, where investors have access to the same information and analyze information in the same manner. Finally, everyone uses the same estimates of expected return and the same variance/covariance matrix.
The APT model works off of the CAPM model, but reduces the number of assumptions. Firstly, it is a multi factor model, of which the portfolio or securities returns follow that theory. Secondly, the investor holds multiple securities, so that unsystematic risk becomes insignificant. Finally, all potential opportunities for riskless profits will be exhausted, essentially causing equilibrium in the market.
The Markowitz model has one major upside, and two major downsides. The upside is its accuracy. This model is the most accurate of the four, due to the fact that it uses so many inputs. Frankly, the more inputs, and the more correct inputs, the more accurate the forecast will be. As far as the downsides, putting in so many values as well as having to research each value to make sure it is the most correct, is extremely time consuming, which means that it can get exponentially costly.
As for the Single-Index model, it works in the opposite way of the Markowitz model. While it is the least time consuming, and therefore the least expensive manner of estimation and forecasting, it is also the least accurate. This is due to the fact that it is generalized as well as it using less data factors as inputs. So, while they may be just as accurate, there is more room for error due to the lack of information quantity and that it does not account for industry wide events, which can have a large impact.
Similarly, the CAPM model has the same issue. While also not as time consuming and...