3 1 reading 40 portfolio risk and return part II pdf

LOS Portfolio Management • • • • • • Portfolio Management – An Overview Portfolio Risk and Return – Part I Portfolio Risk and Return – Part II Basics of Portfolio Planning and Construction Risk Management – An Introduction Fintech in Investment Management LOS LOS Describe the implications of combining a risk-free asset with a portfolio of risky assets • By combining a portfolio of risky assets with a risk-free asset, we can improve the return-risk characteristics of the portfolio resulting in a better trade-off • The combination of risky assets with the risk-free rate results in the Capital Allocation Line (CAL) • The proportion of allocation to risky assets versus allocation to the risk-free asset will be dependent on the risk preferences of the investor • The expected return of the composite portfolio of risky assets and risk-free assets is the weighted sum of the expected returns of the underlying assets Describe the implications of combining a risk-free asset with a portfolio of risky assets • Illustration: The Capital Allocation Line (CAL) is the combination of a risk-free asset and a risky asset The CAL represents multiple portfolios available to the investor E(R p ) Expected return LOS LOS 𝐶𝐴𝐿 𝑅𝑓 𝜎𝑖 𝜎𝑝 LOS LOS Explain the capital allocation line (CAL) and the capital market line (CML) Capital Market Line vs Capital Allocation Line: What’s the Link? • The Capital Market Line (CML) is a special case of the CAL – the line which makes up the allocation between a risk-free asset and a risky portfolio for an investor  In the case of the CML, the risk portfolio is the market portfolio • The investor defines "the market" to be its domestic stock market index; the expected return of the market is expressed as the expected return of that index • The risk-return characteristics for the potential risky asset portfolios can be plotted to generate a Markowitz efficient frontier Explain the capital allocation line (CAL) and the capital market line (CML) Capital Market Line vs Capital Allocation Line: What’s the Link? • The point where the risk-free asset touches, or is tangential, to the Markowitz portfolio, gives the market portfolio The line connecting the risk-free asset with the market portfolio is the CML Expected port return LOS LOS CML Efficient frontier Standard deviation of portfolio 𝜎𝑝 LOS LOS Explain the capital allocation line (CAL) and the capital market line (CML) Calculating return for CML:  The weighted average returns of both the risky and risk-free asset: 𝐄 𝐑 𝐩 = 𝐰𝟏 𝐑 𝐟 + 𝟏 − 𝐰𝟏 𝐄 𝐑 𝐦 Calculating risk for CML: 𝛔𝐩 = 𝟏 − 𝐰𝟏 𝛔𝐦  Note: Since the risk for risk-free asset is zero, we only consider the “risky-asset.” LOS LOS Explain the capital allocation line (CAL) and the capital market line (CML) CML Equation • Equation in the form of Y = a + bx Slope (market price of risk) 𝐄 𝐑𝐩 𝐄 𝐑𝐦 − 𝐑𝐟 = 𝐑𝐟 + × 𝛔𝐩 𝛔𝐦 Example: • Expected return of the risk-free asset: 10% • Expected return of market portfolio: 30%; risk = 40% CML equation: 10% + 30%−10% × 40% σp Explain the capital allocation line (CAL) and the capital market line (CML) CML Drawn 100% in market CML Expected port return LOS LOS 𝐑 𝐦 = 𝟑𝟎% 75% M 50% 0% in market 𝐑 𝐟 = 𝟏𝟎% Standard deviation of portfolio, 𝛔𝐩 LOS LOS Explain the capital allocation line (CAL) and the capital market line (CML) Example: CML Expected return Calculate the expected return with 50% weight invested in the risky asset, given: • Risk free asset: E(R) = 10% • Market portfolio: E(R) = 30%, Risk = 40% Solution Return with 50% in risk-free asset and 50% in the risky asset: = 0.5 × 10% + 0.5 × 30% = 20% LOS LOS Explain systematic and nonsystematic risk, including why an investor should not expect to receive additional return for bearing nonsystematic risk Systematic vs Non systematic (specific) risk • Systematic:  Non-diversifiable market risk  Cannot be avoided  Examples: inflation risk, interest rate risk, business cycle risk, etc • Non-Systematic:  Asset specific risk  Can be diversified away  Examples: Employee go-slow/strike, major oil discovery, recalled product, etc  Investors are ONLY compensated for bearing systematic risk LOS LOS Calculate and interpret beta Examples • Q: Given that risk (standard deviation) of the market is 20%, what is the beta of a $10m Treasury Bill?  Zero (it is risk free) • Q: An asset has a standard deviation of 15% and a market correlation of What‟s the value of beta?  Zero (it has a correlation of zero to the market) • Q: What is beta of an asset with a standard deviation of 15%, a market correlation of 0.8, given that the market std dev is 10%?  Beta = Correlation of asset to market ×Risk of asset Risk of market = (0.8 x 15%)/10% = 1.2 = ρim σi σm LOS LOS Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) What is CAPM all about? • A model to ascertain expected returns of a security/ asset • Primary Determinant: Beta as a capture of systematic risk 𝐄 𝐑 𝐢 = 𝐑 𝐟 + 𝛃𝐢 [𝐄 𝐑 𝐦 − 𝐑 𝐟 )] Assumptions: 1) Investors are risk-averse, rational and utility maximizing  Risk averse: Investors need compensation  Utility maximizing: Every investor wants higher returns  Rational: Every investor analyses available information correctly to arrive at rational decisions LOS LOS Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) CAPM Assumptions cont… 2) Markets are frictionless, including no transaction costs and no taxes  Frictionless: unlimited short selling as well as unlimited borrowing at the risk-free rate  Effects of any transaction costs/taxes are assumed to be immaterial  Restrictions on short selling, however, can impact CAPM by introducing an upward bias in asset prices 3) Investors plan for the same, single holding period  Does not severely limit the applicability of CAPM LOS LOS Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) CAPM Assumptions cont… 4) Investors have homogenous expectations or beliefs  Asset valuations are identical and the same optimal portfolio of risky assets is generated - the market portfolio  Assumption can be relaxed as long as the generated optimal risky portfolios are not significantly different 5) All investments are infinitely divisible  Investors can hold fractions of assets and is convenient from a modeling perspective as it allows for continuous rather than discrete jump functions 6) Investors are price takers  No one investor can influence prices by their trades Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) What’s the Security Market Line?  A representation of CAPM with Beta reflecting systematic risk  Similar to CML: y-intercept = Rf; market risk premium = slope 𝐄(𝐑 𝐢 ) SML Expected return LOS LOS 𝛃𝐢 = 𝛃 𝐦 𝐄(𝐑 𝐦 ) Slope = 𝐑 𝐦 − 𝐑 𝐟 𝐑𝐟 1.0 𝛃𝐢 LOS LOS Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) • The SML is formulated as follows: E(Ri) = Rf + βi[E(Rm) - Rf] where βi = ρi,mσi / σm • Although similar to the Capital Market Line (CML), we have a notable difference:  The CML only applies to portfolios on the efficient frontier providing optimal combinations of risk and return, while the SML applies to any security whether efficient or not Total risk and systematic risk are equal for an efficient portfolio because the nonsystematic risk has been diversified away LOS LOS Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML) How to Calculate expected returns for a security using CAPM? Example Calculate expected returns for a security, given: • R f = 5% • Std dev of security = 40% • Security correlation with market = 0.80 • Std dev of market = 20% • R m = 10% Solution • First, find Beta; Beta = (0.80 x 0.40)/0.20 = 1.6 • Next, use the CAPM model to find the expected return; ER = 5% + 1.6(10% - 5%) = 13% LOS LOS Describe and demonstrate applications of the CAPM and the SML Performance evaluation • Sharpe ratio  Portfolio risk premium divided by the portfolio risk Sharpe ratio = (Rp − Rf)/σp  Slope of the capital allocation line (CAL)  Total risk = systematic + nonsystematic risk  Portfolio with the highest Sharpe ratio has the best performance • Treynor ratio  Similar to Sharpe ratio but only considers systematic risk Treynor ratio = (Rp - Rf) / βp  Does not work for assets with negative betas LOS LOS Describe and demonstrate applications of the CAPM and the SML • M-squared (𝐌 𝟐 ) ratio  The concept behind the M² ratio is to create a portfolio P that mimics the risk of the market portfolio in terms of asset weights  The weight in portfolio P (wp) which sets the portfolio risk equal to the market risk can be written as: wp = 𝜎𝑚 𝜎𝑝 with the balance (1 - wp) invested in the risk-free asset 𝑹𝒑′ = 𝑹𝒇 + 𝝈𝒎 𝑹𝒑 − 𝑹𝒇 𝝈𝒑 𝝈𝒎 𝑴² = (𝑹𝒑 − 𝑹𝒇 ) − (𝑹𝒎 − 𝑹𝒇 ) 𝝈𝒑  A portfolio that matches the return of the market will have a M² value equal to zero while a portfolio that outperforms will have a positive value It is then possible to rank portfolios LOS LOS Describe and demonstrate applications of the CAPM and the SML • Jensen’s alpha  Jensen's alpha can be calculated as: αp = Rp - [Rf + βp(Rm - Rf )]  If αp is positive, the portfolio has outperformed the market whereas as negative value indicates underperformance  The values of alpha can also be used to rank portfolios or the managers of those portfolios with the alpha being a representation of the maximum an investor should pay for the active management of that portfolio LOS LOS Describe and demonstrate applications of the CAPM and the SML Applications of CAPM Securities selection • An asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate  If the observed price is higher than the (CAPM) valuation, then the asset is overvalued and therefore a good sell  If the observed price is lower than the (CAPM) valuation, then the asset is undervalued and therefore a good buy Describe and demonstrate applications of the CAPM and the SML Applications of CAPM Securities selection • An asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate • Undervalued securities appear above the security market line (SML) while overvalued securities appear below the line 𝐄(𝐑 𝐢 ) Expected return LOS LOS SML Undervalued security (good buy) 𝐄(𝐑 𝐦 ) 𝐑𝐟 Correctly valued security Overvalued security (good sell) 𝛃𝐢 LOS LOS Describe and demonstrate applications of the CAPM and the SML Applications of CAPM Portfolio Construction • While constructing a market-replicating portfolio,  Securities with a positive alpha relative to the market index should be included  Securities with negative alpha relative to the index should be excluded, or sold short  To determine the weight of each security within the portfolio, those securities with higher alpha should be given more weight LOS LOS Describe and demonstrate applications of the CAPM and the SML Limitations of CAPM • The true market portfolio includes all assets both financial and nonfinancial, which may not be investable • Different analysts use different proxies for the market portfolio • Beta estimation requires a long history of returns which may not always be available Also history is not a perfect predictor of future outcomes • In reality, investors are unlikely to have homogeneous expectations there will be many optimal risky portfolios and numerous SMLs LOS Portfolio Management • Portfolio Management – An Overview • Portfolio Risk and Return – Part I • Portfolio Risk and Return – Part II  Basics of Portfolio Planning and Construction • Risk Management – An Introduction • Fintech in Investment Management ... optimal risky portfolios and numerous SMLs LOS Portfolio Management • Portfolio Management – An Overview • Portfolio Risk and Return – Part I • Portfolio Risk and Return – Part II  Basics of Portfolio. .. (market price of risk)