Defining Risk
Pertaining the term to the financial world, Risk is defined as uncertainty associated with an investment class that the actual returns will be different from the expected returns, and the investor will lose some or all of the investment amount.
Evolution of the concept of risk
Even though risk has been a part of the investment process since the first ever trade took place in Manhattan on November 13th, 1792, however, the actual documentation of the concept in the form of theory was first postulated by Harry Markowitz in 1954 to what he named as ‘Modern Portfolio Theory’. The theory turned out to be a revolution for the investment community with a simple concept that the portfolio choice of an investor is a trade-off between the expected return and investment risk. However, all investors are risk-averse to a some degree and, therefore, they seek to minimize the risks for any given level of expected return and if exposed to additional risk, investors will demand an additional return to be compensated for assuming higher risk. Even though the trade-off concept is associated with the whole investment community, however, different investors will evaluate the tradeoff differently on an individual risk-aversion basis. In the nutshell, a rational investor will never invest in a portfolio that offers a lower return than the other portfolio that offers higher return, while both the portfolio embeds same level of investment risk.
This led to another important concept of the portfolio theory, ‘The Efficient Frontier’. The efficient frontier is an extremely useful portfolio management tool that proposes that once the risk tolerance of an investor is determined and quantified in terms of standard deviation, the optimal portfolio for the investor can be determined based on his preference for his risk-return class. In other words, the efficient frontier is a set of optimal portfolios that offers risk-return combinations for the investor. At the same time, portfolios that lies below the efficient frontier are sub-optimal and no investor will chose any such portfolio as these portfolios fails to provide enough return at a given level of risk. Similarly, even the portfolio on the efficient frontier that offers a lower return than the other portfolios at a given level of risk will also be classified as sub-optimal.
Highlighted below is an efficient frontier:
As we can see from the diagram above, Portfolio A and Portfolio E are available at the similar risk level, but since Portfolio E offers higher return to the investor, every rational investor will only choose to invest in Portfolio E. Similarly, Portfolio B and Portfolio D are available at the similar risk level, however, since Portfolio D offers higher return, investors will only choose to invest in Portfolio D.
Another important risk related concept proposed in the Modern Portfolio Theory was the diversification. Based on an age old concept of’ Do not put all your eggs in just one basket’, Markowitz documented the diversification concept using the curve shape of the efficient frontier and proposed that an investor can diversify the risk in his portfolio by adding non-correlated stocks as the weighted average risk of non-correlated securities in the portfolio is always less than the weighted average risk of the individual security.
Advancement in the risk related theory
Post the evolution of risk related theory by Markowitz, the next advancement in the field of portfolio management and risk theory was, Capital Asset Pricing Model, popularly known as CAPM. Postulated by William Sharpe in 1960, CAPM is the most eminent advancement of the risk and portfolio theory till date. Taking the theoretical base of Markowitz’s portfolio theory, CAPM Model explained that the composition of optimal risk portfolio is dependent on the future prospects of the security and not on the individual’s own assessment of risk. Accordingly, an investor always chooses his risk exposure through a combination of investment in risk-free assets and risky assets.
Another important development to the risk theory in the CAPM model was the shift from using standard deviation to beta, as a measure of risk. The model asserts that the risk involved in the portfolio is based on how volatile is the portfolio relative to the market index and thus, the risk appraisal was now shifted from the micro-analysis of risk to the macro-analysis of risk embedded in the market index. Beta measures the covariance of security’s return to that of the market index and thus indicates the security’s marginal contribution of risk to the market portfolio of risky securities. Assigning a value of ‘1’ to the beta of the market portfolio, CAPM model asserted that a stock or portfolio with beta greater than 1 indicate that it has higher risk than the market index, while a stock or portfolio with beta greater than 1 indicate that it has lower risk than the market index. Therefore, in an efficient capital market, the risk premium demanded by the investor and the expected return on the security depends on the beta value of the security or the portfolio, and not the standard deviation, as postulated by Markowitz’s Modern Portfolio Theory
Another aspect of risk category that was improvised by CAPM Model was the division of risk into unsystematic risk( non-market risk) and systematic risk(market risk). Developing the Markowitz’s diversification theory, William Sharper agreed that if an investor diversifies across non-correlated assets, the portfolio risk is reduced, however, the risk that is eliminated is unsystematic risk and the risk that remains is systematic risk, which is eventually awarded by the market. Adding further, CAPM asserted that since markets do not reward investors for bearing unsystematic risk, they should add diversify away the unsystematic risk by adding non-correlated stock.
Apart from the improvisation in the quantitative factors of the risk theory, the risk theory has also undergone changes in the field of social sciences. Important to note, unlike the traditional finance field, which assumes that there is a linear relationship between the risk and return measures, behavioral finance provides a closer examination of the risk factors, which the field assumes to be a combination of both subjective and objective factors. While the traditional branch of finance presents risk with a quantitative outlook, behavioral finance takes a different perspective and represents risk through qualitative factors such as the influence of cognitive and emotional factors. Academicians from the field of social studies asserts that the financial and investment risk are situational and based on the multi-dimensional process related to the specific characteristics of the investment product or financial service.
Risk and its related theories are integral part of present day world. Needless to say, with trillions of dollars being invested in the world everyday, risk is undoubtedly an integral part of the evaluation of uncertainty related to those investments. Both, Modern Portfolio Theory(MPT) and its improvised version, Capital Asset Pricing Model(CAPM) are the backbone of the financial decisions being taken by firms around the world. Highlighted below is an example of utilization of the concept of the CAPM model in accessing the required rate of return for a security:
i) Estimation of cost of capital:
Every capital project is appraised on the basis of discount rate that is represented by the weighted average cost of capital(WACC) of the firm. While the cost of debt is available through the company’s annual report, estimation of cost of equity is performed using the CAPM model, which using the beta as a measure of risk involved, estimates the expected return on the equity capital.
Expected Return= Risk free rate+ beta(Return on market index- Risk-free rate)
For instance, a company is willing to appraise a capital project with an initial outlay of -$50,000 and forecasted cash flow of $20000 for three years. The company holds debt worth $25000 at the net interest rate(post tax adjustment) of 4.5%. Additionally, the market value of equity of the company is $80000 and the stock has a beta of 1.2. The risk free rate is 2% and market index return is 7%.
Calculations
In this case, the company will prefer to use Net present value(NPV) method as part of which it will discount the expected cash flows. However, in order to discount the cash flows, the firm will need to calculate the WACC rate:
WACC: Weight of debt* Cost of debt(1-tax rate)+ Weight of equity* Cost of Equity
= 25000/105000* 0.045+ 80000/105000*[0.02+1.2(0.07-0.05)]
= 0.24*0.045+ 0.76* 0.044
= 0.0108+0.03344
= 4.42%
Therefore, now using the WACC rate, the firm can discount the cash flows and see if the NPVs positive for the project.
ii) Identifying the mispriced securities:
Using the CAPM model to calculate the required rate of the security on the basis of beta measure, allows the analyst to identify mispriced securities in the market. Highlighted below is a equity research scenario as part of which, equity analysts can use CAPM model to evaluate the securities:
Risk free rate= 7%
Market index return= 15%
Supportive Calculations:
Forecasted Return: (Forecasted Price-Current Price+ Dividend)/Current Price
Stock A: (27-25+1)/5= 12%
Stock B: (45-40+2)/40= 17.50%
Stock C: (17-15+0.50)/15= 16.60%
Stock A: 7+ 1(15-7)= 15%
Stock B: 7+ 0.8(15-7)= 13.4%
Stock C: 7+ 1.2(15-7)= 16.6%
Analysis:
Stock A: According to beta measure, the stock should earn 15%, however, it is expected to earn 12% only. Therefore, the stock is overvalued.
Stock B: According to beta measure, the stock should earn 13.4%, however, it is expected to earn 17.5%. Therefore, the stock is undervalued.
Stock C: According to beta measure, the stock should earn 16.6% and is even expected to earn 16.6%. Therefore, the stock is properly valued.
References
Efficient Frontier. (n.d.). Retrieved March 10, 2016, from Investopedia: http://www.investopedia.com/terms/e/efficientfrontier.asp
Khatri, D. K. (2010). Portfolio Management. In D. K. Khatri, Security Analysis and Portfolio Management (p. 364). Macmillian.
Nobel Prize. (1990, October 16). Press Release. Retrieved March 10, 2016, from http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1990/press.html
Ricciardi, V. (2008). Risk: Traditional Finance Versus Behavioral Finance. John Wiley and Sons.
Risk. (n.d.). Retrieved March 10, 2016, from Investopedia: http://www.investopedia.com/terms/r/risk.asp
