Central Bank of Egypt The Investment Setting Prepared
Central Bank of Egypt The Investment Setting Prepared & Presented By: Rania Elsawy
Central Bank of Egypt Index I. Introduction to the Investment Setting II. Measures of Risk and Return III. Determinants of Required Rates of Return IV. Relationship between Risk and Return Rania Elsawy 2
Central Bank of Egypt I- Introduction to the Investment Setting • An investment is the current commitment of funds for a period of time in order to derive future payments that will compensate the investor for: 1. 2. 3. The time the funds are committed The expected rate of inflation The uncertainty of future payments • Investors trade a known amount today for some expected future stream of payments Rania Elsawy 3
Central Bank of Egypt I- Introduction to the Investment Setting • Investors invest and want compensation for giving up their savings and deferring their consumption. • Again, they want to be compensated for 1. The time 2. Inflation 3. Uncertainty of return • The sum of these three items is the investors’ required rate of return. Rania Elsawy 4
Central Bank of Egypt II- Measures of Return and Risk • Holding Period Return HPR = Ending Value of Investment/ Beginning Value of Investment • Holding Period Yield HPY = HPR - 1 • Example: If you commit $100 to an investment at the beginning of the year and you get back $110 at the end of the year, what is your holding period yield ? Rania Elsawy 5
Central Bank of Egypt II- Measures of Return and Risk • Annual HPR = HPR 1/n n = number of years the investment is held Example: Consider an investment that cost $250 and is worth $350 after being held for two years HPR = 350/250 = 1. 40 Annual HPR = 1. 401/2 = 1. 1832 Annual HPY = 1. 1832 – 1 = 0. 1832 Rania Elsawy 6
Central Bank of Egypt II- Measures of Return and Risk • In finance, the variance and standard deviation of returns are common measures of investment risk. Both of these are measures of the variability of a distribution of returns about its mean or expected value. • Variance : • Standard deviation: Rania Elsawy 7
Central Bank of Egypt III- Determinants of the Required Rate of Return = Real Risk- Free Rate + Expected Inflation + Risk Premium Rania Elsawy 8
Central Bank of Egypt III- Determinants of the Required Rate of Return • Real Risk Free Rate – Basic interest rate assuming no inflation and no uncertainty about future flows • Expected Inflation – The expected increase in the general level of prices • Risk Premium – A composite of all uncertainty which include 1. 2. 3. 4. 5. Business Risk Financial Risk Liquidity Risk Exchange Rate Risk Country Risk Rania Elsawy 9
III- Determinants of the Required Rate of Return Central Bank of Egypt • Business Risk • Uncertainty of income flows caused by the nature of a firm’s business • Financial Risk • Uncertainty introduced by the method by which the firm finances its investments • Liquidity Risk • Uncertainty introduced by the secondary market for an investment • Exchange Rate Risk • Uncertainty of returns to an investor who acquires securities denominated in a currency different from his or her own • Country Risk • Uncertainty of returns caused by the possibility of a major change in the political or economic environment of a country Rania Elsawy 10
Central Bank of Egypt IV- Relationship between Risk and Return • The expected return of an investment is directly related to its risk. • Risk and return are positively correlated • As risk increases, the possibility of achieving higher returns also increases • Investors are generally risk averse – Given two investments that have equal expected returns, a risk averse investor will choose the one with less risk (standard deviation) Rania Elsawy 11
Central Bank of Egypt IV- Relationship between Risk and Return • Diversification – Allows an investor to reduce portfolio risk without necessarily reducing the portfolio’s expected return – Concept is similar to not putting all of one’s eggs into one basket – Risk averse investors should always attempt to diversify when possible • Unsystematic Risk – Unique risk, diversifiable risk, firm specific risk • Systematic Risk – Nondiversifiable risk, market risk Rania Elsawy 12
Central Bank of Egypt IV- Relationship between Risk and Return Rania Elsawy 13
Central Bank of Egypt IV- Relationship between Risk and Return • Covariance – Measures the extent to which two variables move together over time. It is an absolute measure and is measured in return units squared where: Rt , l = return on Asset 1 in period t R , 2 = return on Asset 2 in period t R 1 = mean return on Asset 1 Rt , 2 = mean return on Asset 2 n = number of periods Rania Elsawy 14
Central Bank of Egypt IV- Relationship between Risk and Return • Correlation – A pure measure of co-movement of the two stocks’ returns and is bounded by -1 and +1 – This relationship can also be written as Rania Elsawy 15
Central Bank of Egypt IV- Relationship between Risk and Return • Correlation – A correlation of +1 • deviations from the mean or expected return are always proportional in the same direction • Perfect positive correlation – A correlation of -1 • Deviations from the mean or expected return are always proportional in the opposite direction • Perfect negative correlation – A correlation of zero • No linear relationship between the two investments • Uncorrelated Rania Elsawy 16
Central Bank of Egypt IV- Relationship between Risk and Return • Variance of the portfolio (composed of two risky assets) Or • Standard deviation of the portfolio (composed of two risky assets) Rania Elsawy 17
Central Bank of Egypt IV- Relationship between Risk and Return • What happens to porfolio risk as correlation varies? • Consider the following example: – Consider two risky assets that have returns variances of 0. 0625 and 0. 0324, respectively. The assets’ standard deviations of returns are then 25% and 18%, respectively. Calculate the variances and standard deviations of portfolio returns for an equal-weighted portfolio of the two assets when their correlation of reutns is 1, 0. 5, 0, and -0. 5. • Will portfolio risk increase or decrease as correlation decreases? Rania Elsawy 18
Central Bank of Egypt IV- Relationship between Risk and Return Rania Elsawy 19
Central Bank of Egypt IV- Relationship between Risk and Return • The lower the correlation of asset returns, the greater the risk reduction (diversification) benefit of combining assets in the portfolio • If assets returns were perfectly negatively correlated, portfolio risk could be eliminated altogether for a specific set of set weights. Rania Elsawy 20
Central Bank of Egypt IV- Relationship between Risk and Return • Assume we vary the weights on the individual assets to determine the combination of portfolios that have the least risk, the lowest standard deviation Rania Elsawy 21
Central Bank of Egypt IV- Relationship between Risk and Return • Indifference curves plot combinations of risk (standard deviation) and expected return among which an investor is indifferent. • The investor’s expected utility is the same for all points along a single indifference curve. Which portfolio will be the most preferred Portfolio to a risk averse investor? Rania Elsawy 22
Central Bank of Egypt IV- Relationship between Risk and Return • • Introducing a risk free asset to our calculations. Asset A will be the risky asset Asset B will be the risk free asset Expected Return • Standard Deviation of the portfolio Standard deviation of risk free asset is zero Rania Elsawy 23
Central Bank of Egypt IV- Relationship between Risk and Return • The line representing all investors’ optimum portfolios with all possible combinations of risk free asset and the optimal risky asset portfolio is referred to as the capital allocation line Rania Elsawy 24
Central Bank of Egypt IV- Relationship between Risk and Return • An investor’s optimal portfolio is the point of tangency between his/her indifference curve and the capital allocation line Point A is the optimal portfolio for Investor A Point B is the otpimal portfolio for Investor B Rania Elsawy 25
Central Bank of Egypt IV- Relationship between Risk and Return • The optimal capital allocation line (CAL) for any investor is the one that is tangent to the efficient frontier. • This line is called the capital market line (CML). Rania Elsawy 26
Central Bank of Egypt IV- Relationship between Risk and Return • The equation of the CML: or -Y-intercept - market risk premium -Risk free rate - slope of the CML Rania Elsawy 27
Central Bank of Egypt IV- Relationship between Risk and Return • Charting the Security Market Line (SML) which measures systematic risk Rania Elsawy 28
Central Bank of Egypt IV- Relationship between Risk and Return • The SML is the least squares regression line. – The line that minimizes the sum of the squared distances of the points plotted from the line – Line of “best fit” Rania Elsawy 29
Central Bank of Egypt IV- Relationship between Risk and Return • The equation of the SML is known as the capital asset pricing model (CAPM) • One of the most fundamental concepts in investment theory where Rania Elsawy 30
Central Bank of Egypt IV- Relationship between Risk and Return • The CAPM – Expected return on risky asset is the risk free rate plus a betaadjusted market risk premium – Beta measures systematic risk • Example: The expected return on the market is 15%, the risk-free rate is 8%, and the beta for risky asset is 0. 8. compute the rate of return that would be expected on this stock? Rania Elsawy 31
Central Bank of Egypt IV- Relationship between Risk and Return • The CAPM and SML are also ways to show if an asset is properly priced, over valued or undervalued • Points that plot above the SML are underpriced and are offering a greater expected return than is required for their systematic risk • Points that plot below the SML are overpriced and are offering a lesser expected return than is required for their systematic risk Rania Elsawy 32
Central Bank of Egypt IV- Relationship between Risk and Return • Is point B overvalued or undervalued? • Is point A overvalued or undervalued? • Is point C overvalued or undervalued? Rania Elsawy 33
Central Bank of Egypt IV- Relationship between Risk and Return • A measure of risk adjusted return is the Sharpe ratio = • Measures excess returns per unit of total portfolio risk Rania Elsawy 34
Central Bank of Egypt IV- Relationship between Risk and Return • When constructing a portfolio for an entity, it is very important to understand the circumstances, objectives, and constraints – RISK OBJECTIVES and specifications for portfolio risk must be determined • Determining risk tolerance is KEY – RETURN OBJECTIVES are maximized with respect to the risk objectives and constraints • Strategic asset allocation is the percentage allocation to various asset classes that is designed to meet the investor’s objectives Rania Elsawy 35
Central Bank of Egypt THANK YOU! Rania Elsawy 36
Central Bank of Egypt SOURCES USED - Investment Analysis and Portfolio Management, Dryden, 6 th Sixth Edition - Schweser Lecture Notes, CFA Level 1, Kaplan 2012 - Stalla Lecture Notes, CFA Level 1, 2007 Rania Elsawy 37
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