Chapter No 5 Investment Analysis and Portfolio Management Portfolio Return Analysis

Introduction to Return

Risk and return are the two most important attributes of an investment. Research has shown that these two are linked in the capital markets and that generally, higher returns can only be achieved by taking on greater risk. Taking on additional risk in search of higher returns is a decision that should not be taking lightly. Introduction to Risk and Return CHAPTER 8 – Risk, Return and Portfolio Theory Return % RF Risk Risk Premium Real Return Expected Inflation Rate

 It is a possibility or certainty of earing profit from a project or business activity for which the analysts and businessmen must have awareness to achieve.  It can be defined as;  The income received on an investment plus any positive change in the market price shares which is usually expressed in percentage of the beginning price of the investment is called return.  Expected Return:  It is the weighted average of possible returns with the weights being the possibilities of occurrence is called expected return. What is return???

 Total return= C.F + P.C/P.P  Where;  C.F= cash payments received over the period  P.C= price change over the period  P.P= purchase price How to calculate total return??

Mr. A invested 500,000 Afs in bonds. The company pays him 12% interest per bond. The initial price of bond= 50 Afs Current price of bond= 60 Afs Find total return ? So we know that T.R= C.F+P.C/P.P To find this we have to follow steps given next Example

Steps of Finding Total Return

Mr. A invested 100,000 Afs in bonds. The company pays him 25% interest per bond. The initial price of bond= 80 Afs Current price of bond= 90 Afs Find total return ? So we know that T.R= C.F+P.C/P.P To find this we have to follow steps given Assignment

How to calculate Actual return Actual return= cash received from investment+ Current price of asset – purchased price of asset divided by purchase price.  A.R = C.F + C.P- P.P P.P

Example  Mr. Ali bought a Taxi at 400,000 AFS. He earned an amount of 250,000 AFS in 2 years by driving it excluding all other expenses he made in care repair etc... The current market price of the Taxi is 350,000 AFS. Find the Actual Return on his investment.  Use given Formula A.R = C.F + C.P- P.P/ P.P  /  =0.5  50%

Assignment  Mr. Ahmad opened school & invested 700,000 AFS. He earned AFS in 3 years excluding all expenses. Now his friend offers him 800,oo0 AFS. Calculate actual Return on his investment.  Use given Formula A.R = C.F + C.P- P.P/ P.P

Measuring Returns

Ex Ante Returns  Return calculations may be done ‘before-the-fact,’ in which case, assumptions must be made about the future Ex Post Returns  Return calculations done ‘after-the-fact,’ in order to analyze what rate of return was earned. Measuring Returns

As we know that the constant growth can be decomposed into the two forms of income that equity investors may receive, dividends and capital gains. WHEREAS Fixed-income investors (bond investors for example) can expect to earn interest income as well as (depending on the movement of interest rates) either capital gains or capital losses Measuring Returns

 Income yield is the return earned in the form of a periodic cash flow received by investors.  The income yield return is calculated by the periodic cash flow divided by the purchase price. Where CF 1 = the expected cash flow to be received P 0 = the purchase price Measuring Returns Income Yield

 For stocks we find dividend yield while for bond we find interest yield.  We can not forecast dividend yield because next year’s dividends cannot be predicted in aggregate as it is paid from the net income.  Reason – risk  The risk of earning bond income is much less than the risk incurred in earning dividend income. (Remember, bond investors are secured creditors. They have first legally-enforceable contractual claim to interest. But stock investors are not secured ) Income Yield Stocks versus Bonds

Investors in market-traded securities (bonds or stock) receive investment returns in two different form:  Income yield  Capital gain (or loss) yield The investor will receive dollar returns, for example:  $1.00 of dividends  Share price rise of $2.00 To be useful, dollar returns must be converted to percentage returns as a function of the original investment. (Because a $3.00 return on a $30 investment might be good, but a $3.00 return on a $300 investment would be unsatisfactory!) Measuring Returns Dollar Returns

An investor receives the following dollar returns a stock investment of $25:  $1.00 of dividends  Share price rise of $2.00 The capital gain (or loss) return component of total return is calculated: ending price – minus beginning price, divided by beginning price Measuring Returns Converting Dollar Returns to Percentage Returns

 The investor’s total return (holding period return) is: Measuring Returns Total Percentage Return [8-3]

 The general formula for holding period return is: Measuring Returns Total Percentage Return – General Formula

 Measurement of historical rates of return that have been earned on a security.  It allows us to identify trends or tendencies that may be useful in predicting the future.  There are two different types of ex post mean or average returns used:  Arithmetic mean  Geometric mean Measuring Average Returns Ex Post Returns

Where: r i = the individual returns n = the total number of observations  Most commonly used value in statistics  Sum of all returns divided by the total number of observations Measuring Average Returns Arithmetic Average

 Measures the average or compound growth rate over multiple periods. Measuring Average Returns Geometric Mean [8-5]

If all returns (values) are identical, the geometric mean = arithmetic average. If the return values are volatile. the geometric mean < arithmetic average The greater the volatility of returns, the greater the difference between geometric mean and arithmetic average. Measuring Average Returns Geometric Mean versus Arithmetic Average

Measuring Average Returns Average Investment Returns and Standard Deviations The greater the difference, the greater the volatility of annual returns.

 While past returns might be interesting, investor’s are most concerned with future returns.  Sometimes, historical average returns will not be realized in the future.  That’s way investors are supposed to calculate expected ex ante returns.  Ex ante return calculation is also called forecasting expected returns. Measuring Expected (Ex Ante) Returns

Estimating Expected Returns Estimating Ex Ante (Forecast) Returns Example: This is type of forecast data that are required to make an ex ante estimate of expected return

Measuring Expected (Ex Ante) Returns  We can calculate it by using two different methods.  1. spread sheet method  2. general formula method.

Estimating Expected Returns Estimating Ex Ante (Forecast) Returns Using a Spreadsheet Approach Example Solution: Sum the products of the probabilities and possible returns in each state of the economy

 The general formula Where: ER = the expected return on an investment R i = the estimated return in scenario i Prob i = the probability of state i occurring Estimating Expected Returns Estimating Ex Ante (Forecast) Returns [8-6]

Estimating Expected Returns Estimating Ex Ante (Forecast) Returns Using a Formula Approach Example Solution: Sum the products of the probabilities and possible returns in each state of the economy