Multi-factor models in finance

1. In finance, a multi-factor model employs various determinants in its calculations to establish a given phenomenon by exploring the underlying relationship of the said determinants. In the case where several microeconomic, statistical, macroeconomic and fundamental factors used to explain an asset’s price, one of the main disadvantages of a multi-factor model is that it only incorporates the use of historical data which may not be accurately given the overview of the future relationship of the said variables, not to mention that the model does not account for non-quantifiable phenomena which when it comes to financial risk, carries a lot of weight.

One of the most commonly used multi-factor models in finance if the three-factor model by Fama and French. This model perfects on the capital asset pricing model (CAPM) by incorporating the aspects of value risk and size risk factors into the market risk factors by the CAPM. This multi-factor model is represented as Rit​−Rft​=αit​+β1​(RMt​−Rft​)+β2​SMBt​+β3​HMLt​+ϵit. In this case, Rit is the expected return of a given security at a specific time; Rft is the risk-free rate at the time; RMt  is the returns of the portfolio; Rit​−Rft is the excess returns expected; RMt​−Rft is the market’s excess returns; SMBt is considered size premium of the security; HMLt is the considered value premium of the security; and β1, β2, β3 are the coefficients of the factors. It is also worth noting that this model has incorporated the use of beta (β), which is another multi-factor model used to determine the riskiness of given security concerning the market, which is usually the S&P 500 index. In the three-factor model by Fama and French, beta is relied upon to determine the sequential coefficients. In itself, beta as a multi-factor model builds on the market returns, usually of the S&P 500,  which is highly diversified, and the market factors affecting the constituent securities vary widely. They often do not have any bearing on one another. This entrenched inequality is carried forward to the three-factor model, which like the beta model, also uses statistical historical values with low predictive qualities since the operating environment is constantly changing. As constituted, the main difficulty with multi-factor models is that they are backward-looking.

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To prove this, the equation ρ(A1+A2)≤ρ(A1)+ρ(A2) VAR is less than the sum of its parts.

3. The assets were chosen at random, representing various industries to create a diversified ETF while the S&P 500 index was used to a gauge metric for the ETF derived from these 20 stocks.