1. An investor does not need to make a decision which portfolio to choose when a risk free asset is included. There is now only one tangent portfolio he can choose. Explain this statement with graphs analysis.
The line of possible portfolio risk and return combinations given the risk-free rate and the risk and return of the portfolio of risky assets is called capital allocation line(CAL). For an individual investors and under the assumption of CAPM model that each investor faces homogeneous expectations, the best capital allocation line is the one that offers the highest expected utility in terms of risk and return. (Standard of Portfolio Management,2013)
(Standard of Portfolio Management,2013)
For instance,in the above graph,of the three portfolios , A, B and C, the optimal portfolio will be one that is tangent to indifference curve, i.e. Portfolio A as it offers maximum utility to the investor by combining the risk free asset with the risky portfolio. (Standard of Portfolio Management,2013)
2. Outline assumptions made in the Capital Asset Pricing Model (CAPM) why they are important and the conclusion reached about the tangent portfolio when these assumptions are made. And write out the CAPM equation. Explain the difference between systematic and unsystematic risk and why only systematic risk is rewarded in CAPM.
About CAPM
Capital Asset Pricing Model(CAPM), is one of the most fundamental and widely used financial model. The model asserts that in equilibrium, the expected return on risky assets is the risk free rate plus market premium adjusted for beta, which measures the systematic risk.(ACCA, 2016)
Below discussed are the assumptions laid down in the CAPM Model:
a)The model aims to maximize the maximum utility for the investors
b) Investors are risk-averse and rationale
c) Investors are price takers and have no influence on the price levels of assets
d) Investors can lend and borrow unlimited funds at the risk free levels
e) All investors receive the same amount of information at the same time
f) There is no transaction cost or taxation, and the capital markets operate perfectly
g) Investors holds a diversified range of assets and are only looking for return because of systematic risk as unsystematic risk is eliminated
(Readyratios.com,2016)
Tangent Portfolio:
One of the simplifying assumptions of CAPM model is that the investors are assumed to have homogeneous expectations, i.e. they have the same estimate of risk, return and correlation with other risky assets for all risky assets. Under this assumption, all investors face the same efficient frontier of risky portfolios and will have the same optimal risky portfolio and capital allocation line. In other words, the capital allocation line that will be tangent to indifference curve will be the optimal one. (Standard of Portfolio Management,2013)
Difference between systematic and unsystematic risk
The total risk involved within the asset class is systematic risk and unsystematic risk. While the latter kind of risk is not based on market and is completely diverisifiable through the process of diversification, on the other hand, systematic risk is completely based on market and cannot be diverisified. Important to note, according to the portfolio theory, investors are only rewarded for bearing systematic risk.(McDill, 2014)
3. The expected return on the market is =0.13 and standard deviation is 0.2 and the variance is 0.04 and risk free rate is 0.04. The covariance for asset 1 is 0.0488 and 0.0392 for asset 2.Caculate betas and expected returns for both assets 1 and 2 using CAPM equation.
a ) BetaAsset 1= Covariance of Asset’s return with the market return/ Variance of market return
= 0.0488/0.04
= 1.22
b) Expected ReturnAsset 1= Risk free rate+ Beta(Market Return- Risk Free Rate)
= 0.04+1.22(0.13-0.04)
= 14.98%
c) BetaAsset 2= Covariance of Asset’s return with the market return/ Variance of market return
= 0.0392/0.04
= 0.98
d) Expected ReturnAsset 2= Risk free rate+ Beta(Market Return- Risk Free Rate)
= 0.04+0.98(0.13-0.04)
= 12.82%
4. Suppose investor now evaluated the realised returns and found answers different from above 3. The realised returns are 0.16 for asset 1 and 0.12 for asset 2. Assuming that the investors believe CAPM is correct are the assets mis-prices relative to the CAPM expected returns? Explain what strategy investor would use to exploit this mis-pricing.
Following the investor’s realized returns and the required returns projected by CAPM model, it is evident that the required return based on systematic risk of Asset 1 is 14.98%, and the realized return is 16%, the stock is undervalued and thus,the investor would go long on Asset 1.
On the other hand,for Asset 2, based on systematic risk, the stock is required to earn 12.82%, but it realized only 12%. This indicates that the stock is overvalued and hence,the investor will go short here.
References
Accaglobal.com. (2016). CAPM: theory, advantages, and disadvantages | F9 Financial Management | ACCA Qualification | Students | ACCA Global. [online] Available at: http://www.accaglobal.com/in/en/student/exam-support-resources/fundamentals-exams-study-resources/f9/technical-articles/CAPM-theory.html [Accessed 23 Jul. 2016].
McDill, K. (2016). Systematic Risk Vs. Unsystematic Risk: Know The Difference. [online] Millionairecorner.com. Available at: http://millionairecorner.com/Content_Free/Systematic-Risk.aspx [Accessed 23 Jul. 2016].
Readyratios.com. (2016). Capital Asset Pricing Model (CAPM). [online] Available at: http://www.readyratios.com/reference/analysis/capital_asset_pricing_model_capm.html [Accessed 23 Jul. 2016].
The standard for portfolio management. (2013). Newtown Square, Pa: Project Management Institute.
