Multifactor Risk Models and Portfolio Construction and Management

Abstract

The previous chapter introduced the reader to Markowitz mean-variance analysis and the Capital Asset Pricing Model. The cost of capital calculated in chapter “Debt, Equity, the Optimal Financial Structure, and the Cost of Funds” assumes that the cost of equity is derived from the Capital Asset Pricing Model and its corresponding beta, or measure of systematic risk. The Gordon Model, used for equity valuation in chapter “The Equity of the Corporation: Common and Preferred Stock,” assumes that the stock price will fluctuate randomly about its fair market value. The cost of equity is dependent upon the security beta. In this chapter, we address the issues inherent in a multi-beta or multiple factor risk model. The purpose of this chapter is to introduce the reader to multifactor risk models. There are academic multifactor risk models, such as those of Cohen and Pogue (1967), Farrell Jr. (1974), Stone (1974), Ross (1976), Ross and Roll (1980), Dhrymes, Friend, and Gultekin (1984), Dhrymes, Friend, Gültekin, and Gültekin (1985), and Fama and French (1992, 1995, 2008). There are practitioner multifactor risk models, such as Barra, created during the 1973–1979 time period; Advanced Portfolio Technologies (APT), created in 1987; and Axioma, created in the late 1990s and gaining practitioner acceptance in the 2000–2019 time period. The former academicians who created these practitioner models are Barr Rosenberg, Andrew Rudd, John Blin and Steve Bender, and Sebastian Ceria. We will introduce the reader to the practitioner models and their academician creators in this chapter. Which models are best? We, at McKinley Capital Management, MCM, have tested these models. None of the models are perfect, but the models are generally statistically significant when the statistically significant tilt variables of chapter “Risk and Return of Equity and the Capital Asset Pricing Model” are used for portfolio construction. In this chapter, we discuss the MCM Horse Races of the 2010–2019 time period to test stock selection within the commercially available multifactor risk models.

Appendices

Appendix 1: US-E3 Descriptor Definitions

This Appendix gives the detailed definitions of the descriptors which underlie the risk indices in US-E3. The method of combining these descriptors into risk indices is proprietary to Barra.

Volatility

• (a) BTSG : Beta times sigma

  This is computed as $\sqrt{{\beta \sigma}_{\varepsilon}}$, where β is the historical beta and σ_ε is the historical residual standard deviation. If β is negative, then the descriptor is set equal to zero.

• (b) DASTD : Daily standard deviation

  This is computed as

  $$ \sqrt{N_{days}\left[{\sum}_{t=1}^T{w}_t{r_t}^2\right]} $$

  where r_t is the return over day t, w_t is the weight for day t, T is the number of days of historical returns data used to compute this descriptor (we set this to 65 days), and N_days is the number of trading days in a month (we set this to 23).

• (c) HILO : Ratio of high price to low price over the last month

  This is calculated as

  $$ \mathit{\log}\left(\frac{P_H}{P_L}\right) $$

  where P_H and P_L are the maximum price and minimum price attained over the last 1 month.

• (d) LPRI : Log of stock price

  This is the log of the stock price at the end of the last month.

• (e) CMRA : Cumulative range

  Let Z_t be defined as follows:

  $$ {Z}_t={\sum}_{s=1}^t\log \left(1+{r}_{\mathrm{i}.\mathrm{s}}\right)-{\sum}_{s=1}^t\log \left(1+{r}_{\mathrm{f},\mathrm{s}}\right) $$

  where r_i,s is the return on stock I in month s and r_f,s is the risk-free rate for month s. In other words, Z_t is the cumulative return of the stock over the risk-free rate at the end of month t. Define Z_max and Z_min as the maximum and minimum values of Z_t over the last 12 months. CMRA is computed as

  $$ \log \left(\frac{1+{Z}_{\mathrm{max}}}{a+{Z}_{\mathrm{min}}}\right) $$

• (f) VOLBT : Sensitivity of changes in trading volume to changes in aggregate trading volume

  This may be estimated by the following regression:

  $$ \frac{\Delta {V}_{\mathrm{i},\mathrm{t}}}{N_{\mathrm{i},\mathrm{t}}}=\mathrm{a}+\mathrm{b}\ \frac{\Delta {V}_{\mathrm{M},\mathrm{t}}}{N_{\mathrm{m}.\mathrm{t}}}+{\xi}_{\mathrm{i},\mathrm{t}} $$

  where ΔV_i,t is the change in share volume of stock I from week t − 1 to week t, N_i,t is the average number of shares outstanding for stock I at the beginning of week t − 1 and week t, ΔV_M,t is the change in volume on the aggregate market from week t − 1 to week t, and N_M,t is the average number of shares outstanding for the aggregate market at the beginning of week t − 1 and week t.

• (g) SERDP : Serial dependence

  This measure is designed to capture serial dependence in residuals from the market model regressions. It is computed as follows:

  $$ \mathrm{SERDP}=\frac{\frac{1}{\mathrm{T}-2}\kern0.5em {\sum}_{t=3}^T{\left({e}_t+{e}_{t-1}+{e}_{t-2}\right)}^2}{\frac{1}{T-2}\kern0.5em {\sum}_{t=3}^T\left({e^2}_t+{e^2}_{t-1}+{e^2}_{t-2}\right)} $$

  where e_t is the residual from the market model regression in month t and T is the number of months over which this regression is run (typically, T = 60 months).

• (h) OPSTD : Option-implied standard deviation

  This descriptor is computed as the implied standard deviation from the Black-Scholes option pricing formula using the price on the closest to at-the-money call option that trades on the underlying stock.

Momentum

• (a) RSTR : Relative strength

  This is computed as the cumulative excess return (using continuously compounded monthly returns) over the last 12 months, i.e.,

  $$ \mathrm{RSTR}\leftarrow ={\sum}_{t=1}^T\log \left(1+{r}_{\mathrm{i},\mathrm{t}}\right)-{\sum}_{t=1}^T\log \left(1+{r}_{\mathrm{f},\mathrm{t}}\right) $$

  where r_i,t is the arithmetic return of the stock in month I and r_f,t is the arithmetic risk-free rate for month i. This measure is usually computed over the last 1 year—i.e., T is set equal to 12 months.

• (b) HALPHA : Historical alpha

  This descriptor is equal to the alpha term (i.e., the intercept term) from a 60-month regression of the stock’s excess returns on the S&P 500 excess returns.

Size

• (a) LNCAP : Log of market capitalization

  This descriptor is computed as the log of the market capitalization of equity (price times number of shares outstanding) for the company.

Size Nonlinearity

• (a) LCAPCB : Cube of the log of market capitalization

  This risk index is computed as the cube of the normalized log of market capitalization.

Trading Activity

• (a) STOA : Share turnover over the last year

  STOA is the annualized share turnover rate using data from the last 12 months—i.e., it is equal to ${\mathrm{V}}_{\mathrm{ann}}/{\overline{N}}_{\mathrm{out}}$, where V_ann is the total trading volume (in number of shares) over the last 12 months and ${\overline{N}}_{\mathrm{out}}$ is the average number of shares outstanding over the previous 12 months (i.e., it is equal to the average value of the number of shares outstanding at the beginning of each month over the previous 12 months).

• (b) STOQ : Share turnover over the last quarter

  This is computed as the annualized share turnover rate using data from the most recent quarter. Let V_q be the total trading volume (in number of shares) over the most recent quarter and let ${\overline{N}}_{\mathrm{out}}$ be the average number of shares outstanding over the period (i.e., ${\overline{N}}_{\mathrm{out}}$ is equal to the average value of the number of shares outstanding at the beginning of each month over the previous 3 months). Then, STOQ is computed as $4{\mathrm{V}}_{\mathrm{q}}/{\overline{N}}_{\mathrm{out}}$.

• (c) STOM: Share turnover over the last month

  This is computed as the share turnover rate using data from the most recent month—i.e., it is equal to the number of shares traded last month divided by the number of shares outstanding at the beginning of the month.

• (d) STO5: Share turnover over the last 5 years

  This is equal to the annualized share turnover rate using data from the last 60 months. In symbols, STO5 is given by

  $$ \mathrm{STO}5=\frac{12\ \left[\frac{1}{T}{\sum}_{s=1}^T\ {V}_s\right]}{\sigma_{\varepsilon}} $$

  where V_s is equal to the total trading volume in month s and ${\overline{N}}_{\mathrm{out}}$ is the average number of shares outstanding over the last 60 months.

• (e) FSPLIT : Indicator for forward split

  This descriptor is a 0–1 indicator variable to capture the occurrence of forward splits in the company’s stock over the last 2 years.

• (f) VLVR : Volume to variance

  This measure is calculated as follows:

  $$ \mathrm{VLVR}=\log \frac{\frac{12}{T}\ \left[{\sum}_{s=1}^T\ {V}_s{P}_s\right]}{\sigma_{\varepsilon}} $$

  where V_s equals the number of shares traded in month s, P_s is the closing price of the stock at the end of month s, and σ_ε is the estimated residual standard deviation. The sum in the numerator is computed over the last 12 months.

Growth

• (a) PAYO: Payout ratio over 5 years

  This measure is computed as follows:

  $$ \mathrm{PAYO}=\frac{\frac{1}{T}{\sum}_{t=1}^T\ {D}_t}{\frac{1}{T}{\sum}_{t=1}^T\ {E}_t} $$

  where D_t is the aggregate dividend paid out in year t and E_t is the total earnings available for common shareholders in year t. This descriptor is computed using the last 5 years of data on dividends and earnings.

• (b) VCAP : Variability in capital structure

  This descriptor is measured as follows:

  $$ \mathrm{VCAP}\leftarrow =\frac{\frac{1}{T-1}{\sum}_{t=2}^T\left(\left|{N}_{t-1}-{N}_t\right|{P}_{t-1}+\left|{\mathrm{LD}}_{t-1}-{\mathrm{LD}}_t\right|+\left|{\mathrm{PE}}_t-{\mathrm{PE}}_{t-1}\right|\right)}{{\mathrm{CE}}_T+{\mathrm{LD}}_T+{\mathrm{PE}}_T} $$

  where N_t−1 is the number of shares outstanding at the end of time t − 1; P_t−1 is the price per share at the end of time t − 1; LD_t−1 is the book value of long-term debt at the end of time period t − 1; PE_t−1 is the book value of preferred equity at the end of time period t − 1; and CE_T + LD_T + PE_T are the book values of common equity, long-term debt, and preferred equity as of the most recent fiscal year.

• (c) AGRO : Growth rate in total assets

  To compute this descriptor, the following regression is run:

  $$ {\mathrm{TA}}_{\mathrm{it}}=\mathrm{a}+\mathrm{bt}+{\upxi}_{\mathrm{it}} $$

  where TA_it is the total assets of the company as of the end of year t and the regression is run for the period = 1, …, 5. AGRO is computed as follows:

  $$ \mathrm{AGRO}\leftarrow =\frac{b}{\frac{1}{T}{\sum}_{t=1}^T{\mathrm{TA}}_{\mathrm{it}}} $$

  where the denominator average is computed over all the data used in the regression.

• (d) EGRO : Earnings growth rate over last 5 years

  First, the following regression is run:

  $$ {\mathrm{EPS}}_{\mathrm{t}}=\mathrm{a}+\mathrm{bt}+{\upxi}_{\mathrm{t}} $$

  where EPS_t is the earnings per share for year t. This regression is run for the period t = 1, …, 5. EGRO is computed as follows:

  $$ \mathrm{EGRO}\leftarrow =\frac{b}{\frac{1}{T}{\sum}_{t=1}^T{\mathrm{EPS}}_t} $$

• (e) EGIBS : Analyst-predicted earnings growth

  This is computed as follows:

  $$ \mathrm{EGIBS}\leftarrow =\frac{\left(\mathrm{EARN}-\mathrm{EPS}\right)}{\left(\mathrm{EARN}\leftarrow +\leftarrow \mathrm{EPS}\right)/2} $$

  where EARN is a weighted average of the median earnings predictions by analysts for the current year and next year and EPS is the sum of the four most recent quarterly earnings per share.

• (f) DELE: Recent earnings change

  This is a measure of recent earnings growth and is measured as follows:

  $$ \mathrm{DELE}\leftarrow =\frac{\left({\mathrm{EPS}}_t-{\mathrm{EPS}}_{\mathrm{t}\hbox{-} 1}\right)}{\left({\mathrm{EPS}}_t+{\mathrm{EPS}}_{t-1}\right)/2} $$

  where EPS_t is the earnings per share for the most recent year and EPS_t−1 is the earnings per share for the previous year. We set this to missing if the denominator is nonpositive.

Earnings Yield

• (a) EPIBS : Analyst-predicted earnings-to-price

  This is computed as the weighted average of analysts’ median predicted earnings for the current fiscal year and next fiscal year divided by the most recent price.

• (b) ETOP : Trailing annual earnings-to-price

  This is computed as the sum of the four most recent quarterly earnings per share divided by the most recent price.

• (c) ETP5 : Historical earnings-to-price

  This is computed as follows:

  $$ \mathrm{ETP}5=\frac{\frac{1}{T}{\sum}_{t=1}^T\ {\mathrm{EPS}}_t}{\frac{1}{T}{\sum}_{t=1}^T\ {P}_t} $$

  where EPS_t is equal to the earnings per share over year t and P_t is equal to the closing price per share at the end of year t.

Value

• (a) BTOP : Book-to-price ratio

  This is the book value of common equity as of the most recent fiscal year end divided by the most recent value of the market capitalization of the equity.

Earnings Variability

• (a) VERN : Variability in earnings

  This measure is computed as follows:

  $$ \mathrm{VERN}=\frac{{\left(\frac{1}{\mathrm{T}-1}{\sum}_{t=1}^T{\left({E}_t-\overline{E}\right)}^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{\frac{1}{T}{\sum}_{t=1}^T{E}_t} $$

  where E_t is the earnings at time t(t = 1, …, 5) and Ē is the average earnings over the last 5 years. VERN is the coefficient of variation of earnings.

• (b) VFLO: Variability in cash flows

  This measure is computed as the coefficient of variation of cash flow using data over the last 5 years—i.e., it is computed in an identical manner to VERN, with cash flow being used in pace of earnings. Cash flow is computed as earnings plus depreciation plus deferred taxes.

• (c) EXTE: Extraordinary items in earnings

  This is computed as follows:

  $$ \mathrm{EXTE}=\frac{\frac{1}{T}{\sum}_{t=1}^T\ \left|{\mathrm{EX}}_t+{\mathrm{NRI}}_t\right|}{\frac{1}{T}{\sum}_{t=1}^T{E}_t} $$

  where EX_t is the value of extraordinary items and discontinued operations, NRI_t is the value of nonoperating income, and E_t is the earnings available to common before extraordinary items. The descriptor uses data over the last 5 years.

• (d) SPIBS : Standard deviation of analysts’ prediction to price

  This is computed as the weighted average of the standard deviation of I/B/E/S analysts’ forecasts of the firm’s earnings per share for the current fiscal year and next fiscal year divided by the most recent price.

Leverage

• (a) MLEV : Market leverage

  This measure is computed as follows:

  $$ \mathrm{MLEV}=\frac{{\mathrm{ME}}_t+{\mathrm{PE}}_t+{\mathrm{LD}}_t}{{\mathrm{ME}}_t} $$

  where ME_t is the market value of common equity, PE_t is the book value of preferred equity, and LD_t is the book value of long-term debt. The value of preferred equity and long-term debt is as of the end of the most recent fiscal year. The market value of equity is computed using the most recent month’s closing price of the stock.

• (b) BLEV : Book leverage

  This measure is computed as follows:

  $$ \mathrm{BLEV}=\frac{{\mathrm{CEQ}}_t+{\mathrm{PE}}_t+{\mathrm{LD}}_t}{{\mathrm{CEQ}}_t} $$

  where CEQ_t is the book value of common equity, PE_t is the book value of preferred equity, and LD_t is the book value of the long-term debt. All values are as of the end of the most recent fiscal year.

• (c) DTOA : Debt-to-asset ratio

  This ratio is computed as follows:

  $$ \mathrm{DTOA}=\frac{{\mathrm{LD}}_t+{\mathrm{DCL}}_t}{{\mathrm{TA}}_t} $$

  where LD_t is the book value of long-term debt, DCL_t is the value of debt in current liabilities, and TA_t is the book value of total assets. All values are as of the end of the most recent fiscal year.

• (d) SNRRT: Senior debt rating

  This descriptor is constructed as a multilevel indicator variable of the debt rating of a company.

Currency Sensitivity

• (a) CURSENS : Exposure to foreign currencies

  To construct this descriptor, the following regression is run:

  $$ {\mathrm{r}}_{\mathrm{i}\mathrm{t}}={\upalpha}_{\mathrm{I}}+{\upbeta}_{\mathrm{i}}{\mathrm{r}}_{\mathrm{mt}}+{\upvarepsilon}_{\mathrm{i}\mathrm{t}} $$

  where r_it is the excess return on the stock and r_mt is the excess return on the S&P 500 Index. Let ε_it denote the residual returns from this regression. These residual returns are in turn regressed against the contemporaneous and lagged returns on a basket of foreign currencies, as follows:

  $$ {\upvarepsilon}_{\mathrm{i}\mathrm{t}}={\mathrm{c}}_{\mathrm{i}}+{\upgamma}_{\mathrm{i}1}{\left(\mathrm{FX}\right)}_{\mathrm{t}}+{\upgamma}_{\mathrm{i}2}{\left(\mathrm{FX}\right)}_{\mathrm{t}-1}+{\upgamma}_{13}{\left(\mathrm{FX}\right)}_{\mathrm{t}-2}+{\upmu}_{\mathrm{i}\mathrm{t}} $$

  where ε_it is the residual return on stock I, (FX)_t is the return on an index of foreign currencies over month t, (FX)_t−1 is the return on the same index of foreign currencies over month t − 1, and (FX)_t−2 is the return on the same index over month t − 2. The risk index is computed as the sum of the slope coefficients γ_i1, γ_i2, and γ_i3—i.e., CURSENS = γ_i1 + γ_i2 + γ_i3.

Dividend Yield

• (a) P_DYLD : Predicted dividend yield

  This descriptor uses the last four quarterly dividends paid out by the company along with the returns on the company’s stock and future dividend announcements made by the company to come up with a Barra-predicted dividend yield.

Non-estimation Universe Indicator

• (a) NONESTU : Indicator for firms outside US-E3 estimation universe

  This is a 0–1 indicator variable: It is equal to 0 if the company is in the Barra estimation universe and equal to 1 if the company is outside the Barra estimation universe.

Appendix 2: Factor Alignment Problems and Quantitative Portfolio Management

Until now, we have discussed Markowitz mean-variance optimization (MVO) framework, evolution of factor models in modeling risk and return, and their application in building reliable and robust expected returns models. Next, we move our focus to the application of factor models within the broader aegis of quantitative portfolio managements (QPM).

Factor models play an integral role in quantitative equity portfolio management. Their applications extend to almost every aspect of quantitative investment methodology including construction of alpha models, risk models, portfolio construction, risk decomposition, and performance attribution. Given their pervasive presence in the field and the natural trend toward specialization, it comes as no surprise that different groups of researchers are often involved in developing factor models for each one of the aforementioned applications.

For instance, a team of quantitative portfolio managers (PM) can develop an in-house model for alpha generation and procure a factor model for purposes of risk management from a third-party risk model vendor. Subsequently, they can combine the two models within the framework of Markowitz mean-variance optimization (MVO) framework to construct optimal portfolios. A completely different factor model can then be used for purposes of performance attribution to identify the key drivers and detractors of performance. Notably, the choice of factors in each one of these factor models need not be identical, thereby introducing incongruity in the portfolio management process. To further complicate the matters, the constraints in the quantitative strategy can introduce additional systematic risk exposures that are not captured by the risk model. The problems that arise due to the interaction between the alpha model, the risk model, and constraints in MVO framework are collectively referred to as factor alignment problems (FAP). Detailed theoretical investigation of FAP and subsequent evolution of augmented risk models has become an interesting line of research in recent years. We refer the readers to Saxena and Stubbs (2012, 2013, 2015), Ceria, Saxena, and Stubbs (2012), and Martin, Saxena, and Stubbs (2013) for detailed analysis on these topics. A brief summary of the key themes is presented next.

We initiate the discussion by focusing on the unconstrained MVO problem, namely,

$$ \operatorname{Maximize}\;\upalpha \ast \mathrm{h}-\left(1/2\right)\ast {\mathrm{h}}^{\mathrm{T}}\ast \mathrm{Q}\ast \mathrm{h}, $$

where α, h, and Q denote the expected returns (referred to as alpha), portfolio holdings, and covariance matrix of returns based on a factor risk model, respectively. Furthermore, let X denote the matrix of risk factors that are used in building the covariance matrix Q. It is instructive to examine the relationship between α and X. Specifically, consider the projection of α on the vector space spanned by the columns of X; the said projection, α_X, is referred to as the spanned component of α, whereas the residual, α_O = α − α_X, is referred to as the orthogonal component. Even though both the spanned and orthogonal components are derived from a common source, namely, α, they have widely different risk characteristics especially when examined through the lens of the covariance matrix Q.

By virtue of being spanned by the risk factors X, the spanned component is deemed to have systematic risk when examined by the risk model. Among other things, this implies that any portfolio exposure to the spanned component is penalized in the MVO optimization framework for both systematic and specific risk. The orthogonal component, on the other hand, is assumed to have no systematic risk since X^T * α_X = 0. This implies that any exposure to the orthogonal component gets a free pass since it is penalized only for the specific risk. Furthermore, as the number of holdings in the portfolio increases, specific risk can asymptotically go down to zero due to diversification benefits. This disparity between the risk treatment of the spanned and orthogonal component creates incentives for the optimizer to the load on the orthogonal component at the cost of exposure to the spanned component.

Such an overloading on the orthogonal component is in itself not particularly troublesome. In fact, if the risk model captures “all” possible sources of systematic risk, such an overloading is completely justified by the portfolio construction philosophy of MVO. Unfortunately, risk models are not designed to capture all sources of risk. Instead, they are designed to capture salient sources of systematic risk and often omit systematic risk factors that are deemed to be insignificant. These design choices are motivated by a variety of reasons including but not limited to statistical power concerns, preference for parsimony, aversion to multi-collinearity, etc. Consequently, choices made during the design of a risk model can result in risk “blind spots,” namely, systematic risk factors that are missing from the risk model. If the alpha model happens to bet on these risk blind spots, the resulting systematic risk exposures will be left untreated during the portfolio construction phase resulting in latent systematic risk exposures. Next, we discuss some of the practical consequences of such latent risk exposures.

Most QPM employ active or total risk constraints. These constraints are meant to limit the volatility of the portfolio and avoid wild swings in portfolio performance. For instance, a portfolio manager (PM) can include an active risk constraint as part of the portfolio construction process to limit the annualized volatility of active returns to be less than or equal to a predetermined limit, say 3%. The expression of this constraint during portfolio optimization necessarily requires a risk model. If the risk and alpha models suffer from FAP, the optimizer will load up on the orthogonal component of alpha, and the realized risk of the portfolio can be significantly higher than 3%. Saxena and Stubbs (2013) studied this phenomenon in detail and found that the divergences in risk prediction that result from FAP tend to be statistically significant and increase during periods of market stress. In other words, presence of FAP can lead of “volatility” surprises in the realized performance of portfolio, and these surprises tend to aggravate during periods of market turmoil. Additionally, they were able to quantify the amount of latent systematic risk in the orthogonal component of alpha and showed that α_O tends to be more volatile than almost half of the risk factors included in a typical commercial risk model. Ceria et al. examine potential sources of latent systematic risk factors and argued that proprietary definitions of well-known factors (momentum, value, growth, etc.) can introduce latent systematic risk factors. In other words, a portfolio manager’s propensity to curate an alpha factor not only leads to better performance (aka alpha) but also introduces latent systematic risk exposures that often go undiagnosed during the portfolio construction process. Martin et al. (2013) examined the role of constraints in FAP and concluded certain kinds of portfolio constraints can also create unintended systematic risk factor exposures which can expose the portfolio to the vagaries of FAP.

Risk underestimation, as discussed here, is merely a symptom of a bigger issue, namely, compromise of the mean-variance optimality of the resulting portfolio holdings. Recall that the primary objective of portfolio optimization is to create a portfolio having an optimal risk-return trade-off. If a portion of systematic risk exposure of the portfolio is inadequately captured by the risk model, then the resulting portfolio cannot be expected to be optimal ex-post, its ex-ante optimality notwithstanding. Factor alignment problems (FAP) symbolizes the difficulty that a portfolio manager (PM) faces in ensuring consistency between the ex-post characteristics of an optimized portfolio and her ex-ante expectations. Lack of alignment between the alpha and risk factors creates risk “blind spots” that get exaggerated by virtue of employing an optimizer. The resulting optimized portfolios take excessive exposure to systematic factors missing from the risk model, thereby compromising the overarching goal of optimal risk-return trade-off, as originally envisaged by Harry Markowitz. Saxena and Stubbs (2015) demonstrate the usefulness of augmented risk models in addressing this issue. Their results indicate that augmenting the risk model with an appropriate augmenting factor not only remedies the risk underestimation problem but also improves risk adjusted returns, thereby restoring the notion of Markowitz efficiency.

Among other things, their results suggest strong synergistic advantages of integrating alpha and risk research processes. In other words, we need to abandon the “one-size-fits-all” approach to risk management and take a more nuanced approach that is sensitive to the specific requirements of a PM. Ultimately, the primary responsibility of a risk model is to capture all un-diversifiable (i.e., systematic) sources of risk that are relevant to a given investment process. A risk model that is constructed in a manner which is agnostic to the very factors that the PM is betting on cannot be expected to accomplish that goal. Augmented risk models partly accomplish this goal and should act as precursor to fully customized risk models that shed the artificial barrier between alpha and risk research and take a holistic view of the investment process.