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Nontraded assets (or: nonmarketable assets or perfectly nonliquid assets) are assets that are not traded on the market. [1] Human capital is the most important nontraded assets. [2] Other important nontraded asset classes are private businesses, claims to government transfer payments and claims on trust income. [3]

## Human Capital & the CAPM

Human capital is the stock of knowledge, habits and social and personality attributes. Its market value (discounted value) of future labour income (a measure of human capital) is greater than the total market value of traded assets. Human capital is also the nontraded asset that is most importable across time. Humans can only hedge their human capital using traded assets by borrowing against labour income (via home mortgages) and by reducing uncertainty via life insurance. However, these hedges are imperfect. Therefore, human capital pressures security prices and thus causes deviations from the Capital Asset Pricing Model (CAPM). [4]

Human capital is the stock of knowledge, habits, social and personality attributes, including creativity, embodied in the ability to perform labor so as to produce economic value. Human capital theory is closely associated with the study of human resources management as found in the practice of business administration and macroeconomics. The original idea of human capital can be traced back at least to Adam Smith in the 18th century. The modern theory was popularized by Gary Becker, an economist and Nobel Laureate from the University of Chicago, Jacob Mincer, and Theodore Schultz. As a result of his conceptualization and modeling work using Human Capital as a key factor, the Nobel Prize for Economics, 2018, was awarded (jointly) to Paul Romer who founded the modern innovation-driven approach to understanding economic growth.

The market value of privately held corporations and businesses is of a similar magnitude as the market value of human capital. However, privately held businesses can more easily hedged using marketable securities and thus are a lesser source of deviations from the CAPM. Privately held businesses have similar risk characteristics as traded assets. Therefore, individuals can partly offset the diversification problems caused by nontraded private businesses by altering their demands for similar, traded assets. [5]

However, the risks of private businesses do differ from those of traded securities. Therefore, a portfolio of traded assets that best hedges the risk of typical private businesses will enjoy excess demand from private business owners. This will cause the price of the assets in this portfolio to be bid up relative to the price predicted by the CAPM ,causing a lower expected return in relation to systematic risk. Conversely, securities with risks highly correlated to the risks of private businesses will have high equilibrium risk premiums, causing a higher expected return in relation to systematic risk; or positive alphas. [6] This has been confirmed by empirical tests by Heaton and Lucas (2000). [7] Thus, private businesses can only be imperfectly hedged using traded securities and therefore still cause deviations from the CAPM. [8]

## The CAPM adjusted for Human Capital

The original CAPM equation is [9]

${\displaystyle E(r_{i})=r_{f}+{\frac {E(r_{m})-r_{f}}{\sigma ^{2}(r_{m})}}cov(r_{i},r_{m})}$

Where E is the expectations operator, ${\displaystyle r_{i}}$ is the end-of-period random yield on the jth asset, ${\displaystyle r_{m}}$ is the end-of-period random yield on the market portfolio and ${\displaystyle r_{f}}$ is one plus the riskless rate of return.

Mayers (1972) has derived a CAPM for an economy in which nontraded assets exist; specifically, an economy in which individuals are endowed with human capital: labor income of varying size relative to their nonlabor income. [10] This model assumes riskless borrowing and lending, thus implying a linear form of the risk expected return relationship, as does the original CAPM. [11] The adjusted CAPM equation becomes, [12]

${\displaystyle E(R_{i})=E(R_{m}){\frac {Cov(R_{i},R_{m})+{\frac {V_{H}}{V_{m}}}Cov(R_{i},R_{H})}{\sigma ^{2}(R_{m})+{\frac {V_{H}}{V_{m}}}Cov(R_{m},R_{H})}}}$

Where ${\displaystyle E}$ is the expectations operator, ${\displaystyle R_{i}}$ is the excess rate of return of the jth asset (${\displaystyle R_{i}=r_{i}-r_{f}}$), ${\displaystyle R_{m}}$ is the excess rate of return on the market, ${\displaystyle R_{H}}$ is the excess rate of return on aggregate human capital, ${\displaystyle V_{H}}$ is the value of aggregate human capital and ${\displaystyle V_{m}}$ is the market value of traded assets (the market portfolio).

In the adjusted CAPM, the beta – the measure of systematic risk – is replaced by an adjusted beta that also accounts for covariance with the portfolio of aggregate human capital. Thus, the model creates a wedge between betas measured against the traded, index portfolio and betas measured against the true market portfolio; the latter also includes human capital (as measured by aggregate labor income). This causes the results to differ in two respects.

First, if the ${\displaystyle Cov(R_{i},R_{H})}$ is positive (as is expected), the adjusted beta is greater when the CAPM beta is smaller than 1 and vice versa. Thus, it is expected that the risk premium will be greater than predicted by the CAPM for securities with a beta less than one and smaller for securities with a beta greater than 1. This results in a less steep security market line (SML). The ratio of ${\displaystyle {\frac {V_{H}}{V_{m}}}}$ may be greater than one and thus likely has a significant economic effect. This may be an explanation for the average negative alpha of high-beta securities and positive alpha of low-beta securities that have been empirically found. [13]

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk. The risk of an individual risky security reflects the volatility of the return from security rather than the return of the market portfolio. The risk in these individual risky securities reflects the systematic risk.

Second, in the adjusted CAPM, the portfolios of maximizing investors are not all identical, as is the case in the original CAPM. [14]

### Jagannathan and Wang’s adjusted CAPM

Jagannathan and Wang (1996) derived an adjusted CAPM where in addition to the beta of the value-weighted stock market index (${\displaystyle \beta ^{vw}}$), they also estimated the betas of assets with respect to labor income growth (${\displaystyle \beta ^{labor}}$). As a proxy for changes in the value of human capital they used the rate of change in aggregate labor income. [15] The resulting adjusted CAPM equation becomes

${\displaystyle E(R_{i})=c_{0}+c_{size}\ln(ME)+c_{vw}\beta ^{vw}+c_{prem}\beta ^{prem}+c_{labor}\beta ^{labor}}$

where ${\displaystyle ME}$ is the market value of the firm's total equity

(Note: Jagannathan and Wang also added a beta reflecting the effect of business cycles on asset returns (${\displaystyle \beta ^{prem}}$).)

## Related Research Articles

Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk.

In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line.

In finance, the beta of an investment indicates whether the investment is more or less volatile than the market as a whole.

In finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance index instead of a market index.

Alpha is a measure of the active return on an investment, the performance of that investment compared with a suitable market index. An alpha of 1% means the investment's return on investment over a selected period of time was 1% better than the market during that same period; a negative alpha means the investment underperformed the market. Alpha, along with beta, is one of two key coefficients in the capital asset pricing model used in modern portfolio theory and is closely related to other important quantities such as standard deviation, R-squared and the Sharpe ratio.

The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expressed as:

The Intertemporal Capital Asset Pricing Model, or ICAPM, is an alternative to the CAPM provided by Robert Merton. It is a linear factor model with wealth as state variable that forecast changes in the distribution of future returns or income.

In corporate finance, Hamada’s equation, named after Robert Hamada, is used to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani-Miller theorem with the capital asset pricing model. It is used to help determine the levered beta and, through this, the optimal capital structure of firms.

Roll's critique is a famous analysis of the validity of empirical tests of the capital asset pricing model (CAPM) by Richard Roll. It concerns methods to formally test the statement of the CAPM, the equation

Capital allocation line (CAL) is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays the return to be made by taking on a certain level of risk. Its slope is known as the "reward-to-variability ratio".

Security characteristic line (SCL) is a regression line, plotting performance of a particular security or portfolio against that of the market portfolio at every point in time. The SCL is plotted on a graph where the Y-axis is the excess return on a security over the risk-free return and the X-axis is the excess return of the market in general. The slope of the SCL is the security's beta, and the intercept is its alpha.

Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference.

Returns-based style analysis is a statistical technique used in finance to deconstruct the returns of investment strategies using a variety of explanatory variables. The model results in a strategy’s exposures to asset classes or other factors, interpreted as a measure of a fund or portfolio manager’s style. While the model is most frequently used to show an equity mutual fund’s style with reference to common style axes, recent applications have extended the model’s utility to model more complex strategies, such as those employed by hedge funds. Returns based strategies that use factors such as momentum signals have been popular to the extent that industry analysts incorporate their use in their Buy/Sell recommendations.

In investing, downside beta is the element of beta that investors associate with risk in the sense of the uncertain potential for loss. It is defined to be the scaled amount by which an asset tends to move compared to a benchmark, calculated only on days when the benchmark’s return is negative.

In investing, dual-beta is a concept that states that a regular, market beta can be divided into downside beta and upside beta. Thus, dual stands for two betas, upside and downside. The fundamental principle behind dual-beta is that upside and downside betas are not the same. This is in contrast to what the Capital Asset Pricing Model assumes, which is that upside and downside betas are identical. Moreover, Fama and French (1992) demonstrated that beta is an imperfect measure of investment risk.

In investing, upside beta is the element of traditional beta that investors do not typically associate with the true meaning of risk. It is defined to be the scaled amount by which an asset tends to move compared to a benchmark, calculated only on days when the benchmark’s return is positive.

## References

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13. Bodie, Z., Kane, A. and Marcus, A. J., 2014. Investments. McGraw-Hill Education: Berkshire.
14. Mayers, D., 1973. Nonmarketable Assets and the Determination of Capital Asset Prices in the Absence of a Riskless Asset, The Journal of Business, Vol. 46, No.2, pp. 258-267.
15. Jagannathan, R. and Wang, Z., 1996. The conditional CAPM and the cross‐section of expected returns. The Journal of Finance, 51(1), pp.3-53.