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The use of the factor model includes 1. Performance analysis on the proportion of portfolio optimization, 2. Deriving the proportion of assets through factor exposure values, 3. Analysis of the phase through economic indicator factors, etc.
[The importance of the Factor model]
The factor model is a model that analyzes the movement, return, and risk of an asset or a portfolio through factors. Generally, regression-based factor models are used for analyzing the expected return and the risk of an asset or a portfolio. An asset’s expected return can be explained by a weighted sum of the expected returns to several market risk factors, such as market indices, and industry factors. style factors, etc, through regression.
The importance of the factor model can be explained in several ways. First, as an investor, it can explain why an asset or a portfolio’s expected return and risk are represented in certain ways. The factor model’s expected returns decompose the expected return on each cross-section of assets into factor-related and asset-specific returns[1]. Also, the risk of an asset or a portfolio can be decomposed into two types of volatility; volatility by the factors - sensitivity to factors (betas) and variance of factors - and volatility by unsystematic (specific) risk. It gives not only the sensitivity of each beta with the portion of volatility assigned by the factors (so the investor can analyze what factors are more sensitive or less) but also how the risk is assigned to the specific risk of an asset or portfolio.
Second, an asset’s ‘individual’ expected return can be explained by ‘diverse’ factors. In the case of the multi-factor model, several factors can explain the asset’s individual expected return, giving insight into yield structure. If the yield structure is specified, the decision-making in asset allocation can be more clear and more explainable. As an institutional investors working in a securities company, it can help the institutional worker to introduce their portfolios to the customers in a better explanation.
Third, the factor model can be used for allocation strategies, additionally with regime analysis (regime-dependent dynamic style allocations model)[2]. The outperformed factors can be analyzed and also the regime periods can be analyzed. With these analyses, the allocation strategies can be conducted with outperformed style factors on each regime being chosen optimally. For instance, an investor might be able to say that ‘value and low volatility were the best style factors in the general period, but quality style factor produced better returns in contraction regime, furthermore, dividend style outperforms in event regimes.’ This analysis can help to make better modeling in some preferred ways such as a defensive portfolio or aggressive portfolio.
Fourth, the factor model can also use the sentiment index as a factor, helping to explain the risk and return of assets by behavioral-based factors. The factors from the market tend to have a high correlation, whereas, the sentiment index factor has a lower correlation with other factors. Of course, PCA for extracting some independent factors can be used for lower correlation, however, these factors by PCA can not be explainable. In the case of the sentiment factor, the explanation of the factor can be clear with a lower correlation with other factors. Also, the Sentiment factor can be used by incorporating other factors to make a better performance. For instance, incorporating sentiment variables into Fama and French five-factor model, it shows that the performance is better than the expected returns[3]. It means that the sentiment factors can help to understand the decision of market participants with better performance.
[1] Connor, G., & Korajczyk, R. A. (2010). Factor models in portfolio and asset pricing theory. In Handbook of portfolio construction (pp. 401-418). Springer, Boston, MA.
[2] Kim, R. (2018). Smart beta strategy and long-short factor investing in style rotation. Korean Journal of Financial Studies, 47(5), 849-891.
[3] Dhaoui, A., & Bensalah, N. (2017). Asset valuation impact of investor sentiment: A revised Fama–French five-factor model. Journal of Asset Management, 18(1), 16-28.
[Factor model utilization 1 – Performance Evaluation of optimized weights]
The first way to use the Factor model is to evaluate the performance of optimized portfolio expected returns. Once we have some optimized weights from the optimization model, such as MVO, GMVP, Black-Litterman model, etc, we can analyze the performance through the Factor model.
Like the picture above, the expected returns of each asset in a portfolio can be analyzed by the factor sensitivities (Matrix β) and expected returns from factors (Matrix E(X)). Through regression, it can analyze not only which factor the expected returns of each asset are more sensitive with (beta) but what factors have more explanatory power on the model (R-Square or Adjusted R-Square). Through this factor model analysis, the performance of the portfolio can be explained in better ways. Additionally, the risk of the portfolio can be decomposed into stock-specific volatility and volatility by Factors through the Factor model. This can also show a better structure of the portfolio's volatility if it is either from stock-specific or Factors.
[Factor model utilization 2 – Derivation of asset allocation through adjustment of specific Factor exposure values for the portfolio]
The second way to use the Factor model is to derivate asset allocation. The allocation can be conducted from determined Factor exposure values. First, there is a case that the portfolio can be made from a combination of different factors[1].
[way1: the combination of factors with low correlation for portfolio factor allocations]
It can be conducted by a combination of style factors, such as value, momentum, and quality factor with equal weights, or a combination of style factors, economical factors, financial factors, or even through PCA or sentimental factors. When it's decided which factors are chosen, correlations between factor returns can be analyzed which can provide diversification benefits. Certain factors can have low correlations with others, suggesting that combining them could yield efficient gain with a diversification effect.
[1] Clarke, R. G., de Silva, H., & Murdock, R. (2005). A factor approach to asset allocation. The Journal of Portfolio Management, 32(1), 10-21.
The table above is an example of analyzing correlations within different factors. Cross-sectional factors seem to have low correlations with systematic market factors, suggesting that the combination of these two factors can have a diversification effect.
Like the above pictures, through each combination of factors with low correlation, Efficient Frontiers can be measured. From the Efficient Frontiers, the optimization problem for portfolio factor allocations can be solved, with or without constraints of return or volatility.
[way2: assets allocation of the portfolio from risk factor exposure]
The other way of using the Factor model with risk factor exposure is to allocate existing assets from the portfolio. It can be conducted during the optimization process with the constraints of factor exposure on each factor. Once the optimization problem gets solved, the weights of portfolio assets that reflect factor exposure on each factor will be calculated. If we find portfolio weights that the overall risk exposure to a specific factor k is equal to zero, it can be neutral to factor k. If the risk exposure to the market factor is equal to zero, it is called market neutral. The advantage of this optimization is that the asset allocation can be conducted with the decision of which factors are more exposed and others are not exposed (neutral to these factors).
[Factor model utilization 3 – Regime analysis from economic Factors]
In selecting an investment model, it may be important to identify the regimes, such as market expansion or contraction. This is because the favorable investment model may vary depending on the regime, and each regime may have better performance in different models. For example, in the regime of economic expansion, the model that takes more volatility to jump on the upward momentum for high expected return, while in the contraction, the low volatility model might be preferred to create a defensive model.
For expecting the current or upcoming regime to prepare the optimized asset allocation for a specific regime, economical Factors can be used. Either from NBER or the stock market index (such as S&P500), the historical regimes can be defined, and the current (if the current regime is not informed yet) or upcoming regime can be predicted from Factors beforehand. The preferred model for each regime can be analyzed from historical performance, so when the signal of regime switching is visible, rebalancing can be carried out in advance. Through this, the optimal model suitable for each regime can be chosen for better performance.