1. Introduction to Financial Management FIN 102 – 5 th Week of Class Dr. Andrew L. H. Parkes “A practical and hands on course on the valuation and financial management of corporations”

2. Intro. to Financial Managment - 5th Week of Class2 Returns and Volatility  Expected Returns  Risk  Diversification Three Basic Topics:

3. Intro. to Financial Managment - 5th Week of Class3 Investment returns  The return R on any investment in shares per period “t” is:  The dividend D t in that period plus the “capital gain/loss” in value of the share (P t - P t-1  The dividend D t in that period plus the “capital gain/loss” in value of the share (P t - P t-1 )  R t = (D t + (P t - P t-1 )) / P t-1

4. Intro. to Financial Managment - 5th Week of Class4 Of course investors look ahead and thus use expected values…  Expected Return= R j 1 * P j 1 + … + R j n * P j n  With R j 1 = Return of share j at expected value 1 Expected Rate of Return Rate of Return (%) 100150-70 Firm X Firm Y  With P j 1 = The probability of between (0 - 100%) that Return 1 will occur for share j

5. Intro. to Financial Managment - 5th Week of Class5 Probability distributions A listing of all possible outcomes, and the probability of each occurrence. A listing of all possible outcomes, and the probability of each occurrence. Can be shown graphically. Can be shown graphically. Expected Rate of Return Rate of Return (%) 100150-70 Firm X Firm Y

6. Intro. to Financial Managment - 5th Week of Class6 What is investment risk? There are two types of investment risk There are two types of investment risk –Stand-alone risk and –Portfolio risk Investment risk is related to the probability of earning a low or negative actual return. Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment. The greater the chance of lower than expected or negative returns, the riskier the investment.

7. Intro. to Financial Managment - 5th Week of Class7 Selected Realized Returns, 1926 – 2001 Average Standard Average Standard Return Deviation Return Deviation Small-company stocks17.3%33.2% Large-company stocks12.720.2 L-T corporate bonds 6.1 8.6 L-T government bonds 5.7 9.4 U.S. Treasury bills 3.9 3.2 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28.

8. Intro. to Financial Managment - 5th Week of Class8 Investment alternatives EconomyProb.T-BillHTCollUSRMP Recession0.18.0%-22.0%28.0%10.0%-13.0% Below avg 0.28.0%-2.0%14.7%-10.0%1.0% Average0.48.0%20.0%0.0%7.0%15.0% Above avg 0.28.0%35.0%-10.0%45.0%29.0% Boom0.18.0%50.0%-20.0%30.0%43.0% Where Prob. Is probability, T-Bill is a US Treasury Bill, HT is High Tech, Coll is a Collections Agency, USR is a Rubber Company and MP is a market Portfolio.

9. Intro. to Financial Managment - 5th Week of Class9 Now Each Group Calculate the Return for Security – Today’s Quiz That is use the formula for the expected return. That is use the formula for the expected return. Then calculate the risk – how? Use the standard deviation formula: Then calculate the risk – how? Use the standard deviation formula: The σ (standard deviation) is a measure for risk (the root of variance): The σ (standard deviation) is a measure for risk (the root of variance): You remember from Statistics class: You remember from Statistics class: σ =√(R j i – R (expected) ^2*P j i

10. Intro. to Financial Managment - 5th Week of Class10 Comparing risk and return Security Expected return Risk, σ T-bills8.0%0.0% HT17.4%20.0% Coll*1.7%13.4% USR*13.8%18.8% Market15.0%15.3% * Seem out of place.

11. Intro. to Financial Managment - 5th Week of Class11 Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? T-bills will return the promised 8%, regardless of the economy. No, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. T-bills are also risky in terms of “reinvestment” rate risk. However, T-bills are risk-free in the default sense of the word.

12. Intro. to Financial Managment - 5th Week of Class12 How do the returns of HT and Coll. behave in relation to the market? HT – Moves with the economy, and has a positive correlation. This is typical – called “CYCLICAL”. HT – Moves with the economy, and has a positive correlation. This is typical – called “CYCLICAL”. Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual. Kind of like this => Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual. Kind of like this =>

13. Intro. to Financial Managment - 5th Week of Class13 Comparing standard deviations USR Prob. T - bill HT 0 8 13.8 17.4 Rate of Return (%)

14. Intro. to Financial Managment - 5th Week of Class14 Comments on standard deviation as a measure of risk Standard deviation (σ i ) measures total, or stand- alone, risk. Standard deviation (σ i ) measures total, or stand- alone, risk. The larger σ i is, the lower the probability that actual returns will be closer to expected returns. The larger σ i is, the lower the probability that actual returns will be closer to expected returns. Larger σ i is associated with a wider probability distribution of returns. Larger σ i is associated with a wider probability distribution of returns. Difficult to compare standard deviations, because return has not been accounted for. Difficult to compare standard deviations, because return has not been accounted for.

15. Intro. to Financial Managment - 5th Week of Class15 Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return. Calculate the Coefficient of Variation for your stock NOW!

16. Intro. to Financial Managment - 5th Week of Class16 Risk rankings, by coefficient of variation CV CV T-bill0.000 HT1.149 Coll.7.882 USR1.362 Market1.020 Collections has the highest degree of risk per unit of return. HT, despite having the highest standard deviation of returns, has a relatively average CV.

17. Intro. to Financial Managment - 5th Week of Class17 Illustrating the CV as a measure of relative risk σ A = σ B, but A is riskier because of a larger probability of losses. In other words, the same amount of risk (as measured by σ) for less returns. 0 AB Rate of Return (%) Prob.

18. Intro. to Financial Managment - 5th Week of Class18 Investor attitude towards risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.

19. Intro. to Financial Managment - 5th Week of Class19 Homework assignment EACH GROUP MUST DO THEIR OWN WORK! Download the daily closing share prices of the shares of your company from yahoo finance over FY 2002 - 2006 and this year up to now Download the daily closing share prices of the shares of your company from yahoo finance over FY 2002 - 2006 and this year up to now What was the average share price in FY 2002 – today? What was the average share price in FY 2002 – today? What was the standard deviation of the share price movement in these years What was the standard deviation of the share price movement in these years Calculate for each year the Coefficient of variation (σ/ R (average) ) – R &  for each year too! Calculate for each year the Coefficient of variation (σ/ R (average) ) – R &  for each year too! Look at your results; Do you conclude that your company’s shares are a high risk investment? Look at your results; Do you conclude that your company’s shares are a high risk investment? Motivate your answer…. Motivate your answer…. 5 points!

20. Intro. to Financial Managment - 5th Week of Class20 Homework Assignment: Prove that a portfolio reduces risk You are investment banker and have to advise your customers on picking the right shares You are investment banker and have to advise your customers on picking the right shares You want to show your customers that taking shares of different reward/risk profiles considerably reduces risk You want to show your customers that taking shares of different reward/risk profiles considerably reduces risk The reward of a share is its R - % return per annum The reward of a share is its R - % return per annum The risk of a share is its standard deviation - in % over the years The risk of a share is its standard deviation - in % over the years NOW: NOW: Take a share that you know and calculate R over 2002 – 2006 Take a share that you know and calculate R over 2002 – 2006 Then invent another stock that has the same mean R (return) over the years but opposite R in some years Then invent another stock that has the same mean R (return) over the years but opposite R in some years Show that investing 50:50 in this stock (which are perfectly negatively correlated in R) creates the same mean Return over the years at a considerable lower risk (standard deviation) as opposed to putting all money in the first stock! Show that investing 50:50 in this stock (which are perfectly negatively correlated in R) creates the same mean Return over the years at a considerable lower risk (standard deviation) as opposed to putting all money in the first stock! Next, do the same for a perfectly positively correlated stock and a set of 2 shares that are somewhat postively correlated but not perfectly… Next, do the same for a perfectly positively correlated stock and a set of 2 shares that are somewhat postively correlated but not perfectly… Finally, answer the question: Are your findings the same? Finally, answer the question: Are your findings the same? 5 points!

21. Intro. to Financial Managment - 5th Week of Class21 Here is how you diversify: Gather information about the share of your team ’ s company and of a company in another industry over the past 5 years Gather information about the share of your team ’ s company and of a company in another industry over the past 5 years You will need the Return per year and the standard deviation over 5 years calculated for your team ’ s company You will need the Return per year and the standard deviation over 5 years calculated for your team ’ s company Now assume you will form a portfolio that consists of 50% of the investment in your company and 50% in the other company Now assume you will form a portfolio that consists of 50% of the investment in your company and 50% in the other company Next calculate the Return again and the Standard deviation Next calculate the Return again and the Standard deviation Prove that the portfolio has reduced your risk! (reduced the value of your standard deviation) Prove that the portfolio has reduced your risk! (reduced the value of your standard deviation) 5 points!

22. Intro. to Financial Managment - 5th Week of Class22 Share X and Y are perfectly negatively correlated Stock X and Y are Perfectly Negatively Correlated Year Share X Share Y R%R%P% 199940-1015 2000-104015 200135-515 2002-53515 2003151515 mean151515 stdev22.6384622.638460 Corr. NO RISK!

23. Intro. to Financial Managment - 5th Week of Class23 X and Y are perfectly positively correlated Stock X and Y are exactly the same and Pertfectly Positively Correlated YearXYPortfolio R%R%P% 1997404040 1998-10-10-10 1999353535 2000-5-5-5 2001151515 mean151515 stdev22.6384622.6384622.63846 Corr.1 Same risk as if 100% put in one of the 2 shares!

24. Intro. to Financial Managment - 5th Week of Class24 X and Y are somewhat correlated YearXYR%R%P% 1997402834 1998-10205 1999354138 2000-5-17-11 20011539 mean151515 stdev22.6384622.5721120.62765 R0.665365 Even at 66% positive correlation, risk is reduced. By taking 2 different shares at negative 66% risk reduces dramatically!

25. Intro. to Financial Managment - 5th Week of Class25 So we can reduce risk by… Putting different stocks in one portfolio Putting different stocks in one portfolio The more different stocks we put in the portfolio the more we can diversify and reduce the risk of the investment. The more different stocks we put in the portfolio the more we can diversify and reduce the risk of the investment. This is called diversification This is called diversification In this way we can diversify all the so called “unsystematic risk” away. In this way we can diversify all the so called “unsystematic risk” away. The systematic risk we will not be able to reduce, as systematic risk is a result of: The systematic risk we will not be able to reduce, as systematic risk is a result of: –Economic and monetary climate changes –Changes in tax regimes of countries –Changes in world oil prices, etc. All securities will be influenced by these “market” factors and as a result all investments have some risk … All securities will be influenced by these “market” factors and as a result all investments have some risk …

26. Intro. to Financial Managment - 5th Week of Class26 End of the first part of Chapter 5 Don’t forget your homework for Wednesday!