**Question:**

Explain and graphically depict how Security Market Line (SML) is different from Capital Market Line (CML). Identify and discuss the importance of minimum variance portfolios? Why CAPM equation might be more relevant than other equations when calculating required rate of return.

### Important notes regarding Assignment:

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## Answer:

### Introduction

The present report aims to conduct comparative analysis of security market line and capital market line to identify differences among these two approaches by using appropriate graphs. Further, this considers the meaning, importance and relevance of the minimum variance portfolio for investors. Last part of the study describes the relevance of capital asset pricing model for evaluation of securities.

### Security Market Line vs Capital Market Line

The Security Market Line (SML) is a graphical portrayal of the capital asset pricing model, i.e. CAPM. It represents the relationship between a security’s expected return and its risk gauged by its beta coefficient. When utilized in portfolio management, this line denotes the opportunity cost of an investment (Sharpe, 2017). The Y-axis (at point where beta is 0) of the SML and it is equivalent to the risk-free rate of interest. SML’s slope is similar to the market premium risk and shows the risk-return trade-off during a specific time.

SML: E (R_{i}) = R_{f} + ?_{im} (E(R_{m}) – R_{f})

Figure 1: Security Market Line

(Source: Sharpe, 2017)

If Beta = 1, then it means that securities are as risky as the market

If Beta > 1, then Securities A and B are riskier in comparison to the market

If Beta < 1, then Security C is less risky in comparison to the market

Capital Market Line (CML) is a graph reflecting the anticipated return of a portfolio comprising every plausible percentage between a market portfolio and risk-free asset. The diversified market portfolio has an only systematic risk and its anticipated return is equivalent to the likely market return in general. Every point along the CML has a high risk-return profile to any portfolio on the efficient border. The CML is regarded to be greater than the efficient frontline as it is supported by the inclusion of a risk-free asset in the portfolio (Sornette, 2017).

CML: E(r_{c}) = r_{F} + ?_{c} E(r_{M}) – r_{F} / ?_{M}

_{}

Figure 2: Capital Market Line

(Source: Sornette, 2017)

Line from RF to L is capital market line.

x = risk premium

= E(R_{M}) – RF

y = risk = ?_{M}

Slope = x/y

= [E(R_{M}) – R_{F}]/ ?_{M}

y-intercept = RF (Sornette, 2017)

One of the key differences between SML and CML is the manner in which risk elements are measured. Beta coefficient is the measure of risk elements in the SML. In contrast, standard deviation determines the risk factors for CML. The SML assesses risk via beta which assists in identifying of risk contribution by the individual security to the whole portfolio. On the other hand, assessment of risk in CML is done by means of standard deviation or via a total risk factor (Hong and Sraer, 2016).

While the SML defines both non-efficiency as well as efficiency of portfolios, while the CML only shows efficient portfolios. When computing of return, the likely return of the portfolio for CML is demonstrated alongside the Y-axis. In contrast, the return on securities for SML, is demonstrated alongside Y axis. For CML, a portfolio’s standard deviation is demonstrated along the Y-axis. On the other hand, for SML, the Beta of security is demonstrated along the X-axis (Pilbeam, 2018).

Where the CML determines the risk-free assets and market portfolio, all security elements are identified by the SML. Unlike the CML, the SML portrays the likely returns of individual assets. The CML identifies the return or risk for efficient portfolios, and the SML shows the return or risk for individual shares (Sharpe, 2017). The bottom line is that the CML is regarded to be better when assessing risk elements.

### Importance of Minimum Variance Portfolios

A minimum variance portfolio is a pool of investments with the least volatility, i.e. those investments which they have less possibility of price variation because they carry the minimum sensitivity risk. The spread of investments combined together has a lower consequent risk level relative to the individual risk of every stock. Investors who are not willing to assume big risks must contemplate taking a minimum variance portfolio (Yang, Couillet and McKay, 2015).

Figure 3: Minimum Variance Portfolio

(Source: Yang, Couillet and McKay, 2015)

A minimum variance portfolio is where the curve turns, wherein the variance is the least. Such a portfolio is often the perfect choice for investors who are nearing their sixties and want a safe investment they can depend on after their retirement. A minimum variance portfolio has assets that are individually volatile, but when clubbed together lead to the least possible degree of risk for the expected rate of return. With such a portfolio, the investor hedges every investment with a compensating investment (Maillet, Tokpavi and Vaucher, 2015).

The minimum variance portfolio loads up on stocks which have low volatility and co-variances. In theory, people may expect such a portfolio to give low returns. However, it turns out that stocks are having a low variance or low beta witness higher returns relative to high-beta or high variance stocks. This is also recorded in the literature as the low volatility anomaly. Resultantly, many ETFs and funds have been introduced in the past few years to exploit the phenomenon (Bodnar, Mazur and Okhrin, 2017).

Over the last four decades, high variance and high beta securities have significantly underperformed low beta and low variance stocks in the American markets. There is an explanation which merges the average investor’s choice for risk and the classic institutional investor’s directive to maximize the ratio of surplus returns and monitoring error compared to a fixed standard without resorting to leverage. Frameworks of delegated asset management depict that these directives dissuade arbitrage in both low beta - high alpha, and high beta - low alpha securities (Kempf and Memmel, 2006). This reasoning is in alignment with many facets of the low variance anomaly entailing why it has fostered in the past few years even as the dominance of institutional investors has increased.

Minimum market portfolios are more flexible in market downturns. As the business cycle finally recoups, a minimum variance portfolio tends to ensure compounding performance in comparison to return provided by market. One of the biggest advantages of the minimum variance portfolio is that it really eliminates expected returns from the optimization which are tough to handle. As the minimum variance portfolios have the sole goal of decreasing risk, instead of striving to optimize the reward-risk ratio. Further, minimum variance portfolio optimization results in noticeable attention on low variance securities in against of the cost of exploiting correlation properties (Clarke, De Silva and Thorley, 2011). While MVP is not ideal portfolios, but they might be appropriate for investors who intend to load up on low-risk stocks. As estimation risk natural to projected returns is a known aspect, the fact that the MVP depends just on risk criteria is an attractive attribute.

### The relevance of the CAPM equation

The Capital Asset Pricing Model (CAPM) is a framework which computes the expected return on the basis of the projected rate of return on the market, the beta coefficient of the security and risk-free rate. The equation for CAPM to calculate the rate of return is

E(R) = R_{f} + ? (R_{market} – R_{f})

The CAPM is a key domain of financial management. Indeed, it has even been proposed that financial management only turned into an academic discipline after William Sharpe released his derivation of the CAPM in the year 1964 (Kerzner and Saladis, 2017).

The Weighted Average Cost of Capital (WACC) method can be employed as the discount rate in investment evaluation, given some restrictive presumptions are satisfied. These presumptions are basically claiming that WACC can be utilized as the discount rate given that the investment project does not alter either the financial or the business risk of the investing party. If the business risk of the investment mosaic is not the same as that of the investing entity, the CAPM can be utilized to compute a discount rate specific to the project (Barberis et al., 2015). The advantage of utilizing a CAPM-obtained project discount rate is shown in Figure 4. Utilizing the CAPM will result in sound investment decisions than utilizing the WACC in the two coloured areas, which can be signified by projects A and B.

Project A will be declined if WACC is employed as the discount rate because the project’s IRR is less than WACC. This decision is not correct, but, since project A will be accepted if a CAPM-obtained specific discounting rate is utilized because the IRR of the project is above the SML. The project promises to provide a greater return than required to counterbalance for its degree of systematic risk and conceding it will raise the shareholder's wealth.

Project B will be accepted if WACC is used as the discounting rate as its IRR is higher than the WACC. This decision would also be wrong. However, since project B would be declined if employing a CAPM obtained discounting rate because the IRR of the project does not provide enough compensation for its degree of systematic risk.

Figure 4: CAPM vs WACC

(Source: Benninga, 2010)

The CAPM model has many merits over other techniques including WACC and DGM for computing expected return, justifying why it has been commonly used for over four decades now:

- It only considers systematic risk, showing a real scenario in which majority investors have a diverse portfolio supported by elimination of unsystematic risk in an essential manner.
- It is a theoretically obtained relationship among expected return and systematic risk. This approach is prone to regular empirical testing and research (Kerzner and Saladis, 2017).
- It is often viewed as a much advanced and better technique to calculate the cost of equity in comparison to the Dividend Growth Model (DGM) in that it clearly considers a firm’s degree of systematic risk compared to the share market as a whole.
- It is evidently better than WACC in offering discount rates for utilization in investment evaluation.
- When businesses examine prospects, if the business combination and financing vary from the existing business, then other expected return computations like WACC are rendered useless. However, CAPM can be used in this situation (Bekaert and Hodrick, 2017).

The bottom line is that no model is ideal. However, each must have some attributes which render it helpful and suitable. CAPM, though criticized for some of its unrealistic presumptions, offers a more usable result than either WACC or DDM in many scenarios. It is stress-tested and easily computed, and when employed together with other elements of an investment mosaic, it can offer unmatched yield data which can remove or support a likely investment (Petty et al., 2015).

## Conclusion

By considering the present study conclusion can be drawn that SML and CML both assist in evaluating efficiency on portfolios but on the basis of different backgrounds. By the application of the minimum variance portfolio, an investor can attain expected returns from the optimization which are tough to handle. Further, CAPM is viable in comparison to other equations as it covers overall aspects concerned with the market for analysis of securities.

## References

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Bekaert, G. and Hodrick, R., 2017. International financial management. Cambridge University Press.

Benninga, S., 2010. Principles of finance with excel. OUP Catalogue.

Bodnar, T., Mazur, S. and Okhrin, Y., 2017. Bayesian estimation of the global minimum variance portfolio. European Journal of Operational Research, 256(1), pp.292-307.

Clarke, R., De Silva, H. and Thorley, S., 2011. Minimum-variance portfolio composition. Journal of Portfolio Management, 37(2), p.31.

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Maillet, B., Tokpavi, S. and Vaucher, B., 2015. Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach. European Journal of Operational Research, 244(1), pp.289-299.

Petty, J.W., Titman, S., Keown, A.J., Martin, P., Martin, J.D. and Burrow, M., 2015. Financial management: Principles and applications. Pearson Higher Education AU.

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Sharpe, W., 2017. Capital Market Theory, Efficiency, and Imperfections. Quantitative Financial Analytics: The Path to Investment Profits, p.445.

Sornette, D., 2017. Why stock markets crash: critical events in complex financial systems. Princeton University Press.

Yang, L., Couillet, R. and McKay, M.R., 2015. A robust statistics approach to minimum variance portfolio optimization. IEEE Transactions on Signal Processing, 63(24), pp.6684-6697.