1. SECTION 2: IMPORTANCE OF CAPITAL MARKET HISTORY 1Prepared by Alhaj Nuhu Abdulrahman Measuring stock historical Returns: Investors buy stocks in anticipation of returns. The returns come in the form dividend and/or capital gain or loss. The total return therefore is comprised of dividend and capital gain or loss. Cash returns: If cash returns are considered, then if you bought 1,000 shares of a company at the beginning of the year for say GH¢12.50 per share, the total value of the investment would be: Co = 1,000 x GH¢12.50 = GH¢12,500. Suppose by the end of the year a dividend of GH¢1.40 per share was paid, your total dividend income should be: D = 1,000 x GH¢1.40 = GH¢1,400. Suppose, at the end of the year the share price increased to GH¢14.00. Because of the price increase, you have a capital gain of:

2. Measuring stock historical Returns Gain = (GH¢14.00 - GH¢12.50 = GH¢1.50) x 1,000 = GH¢1,500 However, if the price had fallen to say GH¢11.80, you would have made a capital loss of: Loss = (GH¢11.80 - GH¢12.50 = -GH0.70) x 1,000 = -GH¢700 The total cash return on the investment is thus, dividend income + capital gain/loss, which is GH¢1,400 + GH¢1,500 = GH¢2,900 for one year investment called holding period. Or GH¢1,400 + (- GH¢700) = GH¢700. Percentage returns It is however more convenient to compute and express returns in percentage terms than in cash. In the illustration above, the beginning price was GH¢12.50 per share and dividend GH¢1.40. 2Prepared by Alhaj Nuhu Abdulrahman

3. Measuring stock historical Returns Percentage income return also called dividend yield is; = 11.20% Percentage capital gain yield = = 12% Total percentage return = = = = = 23.20% Thus Total cash return = Total percentage return x Investment = 23.20% x GH¢12,500 = GH¢2,900 3Prepared by Alhaj Nuhu Abdulrahman

4. Average Returns (Holding Period Returns) The returns discussed above are for one year investment called one holding period return (HPR) or simply R. However assuming the GH¢12,500 investment is for 4 years and each year’s percentage return calculated as 23.20%, 20.50%, -10.40% and 21.30% respectively, then we have a 4-year period. They can be expressed as HPR 1 23.20%, HPR 2 20.50%, HPR 3 -10.40% and HPR 4 21.30%. A close study of the 4 yearly returns reveal changes in them. The changes are the variability of returns. Given these variability you might be interested in knowing the average return for the 4-yearly investment returns by means of Arithmetic Average Returns (AAR) and Geometric Average Return (GAR). 4Prepared by Alhaj Nuhu Abdulrahman Measuring stock historical returns

5. Arithmetic Average Return (AAR) ARR = = = = = 13.65% Geometric Average Return (GAR) The arithmetic average return (AAR) of 13.65% calculated above assumes that the yearly returns were not re-invested in more shares. The geometric average return (GAR) however assumes re-investment of the yearly returns and the original investment amount does not change. GAR = = 5Prepared by Alhaj Nuhu Abdulrahman

6. Measuring stock historical returns Geometric Average Return (GAR) = = (1.613491067) 0.25 – 1 = 1.127045998 – 1 = 12.70% Or GAR = 6Prepared by Alhaj Nuhu Abdulrahman

7. Measures of Historical Variability (Risk) of Returns The most common measures of variability (risk) of returns from the mean (average) are the statistical variance (σ 2 ) and its square root the standard deviation (σ). Thus, the historical risk of our example will be computed as follows: σ 2 = = = = σ = = 16.07% 7Prepared by Alhaj Nuhu Abdulrahman

8. Assume you bought the shares of YogoMilk company five years ago at the price of GH¢10 per share. The past five-year investment generated the following yearly cash returns: Year 0 1 2 3 4 5 Share Price (¢) 10 7 12 11.50 11 12 Div. Received (¢) ---- 1.00 1.00 0.90 0.90 1.10 Use the cash returns to calculate; 1) The yearly Holding Period Returns (HPRs) 2) The Arithmetic Average Return (AAR) 3) The Geometric Average Return (GAR) 4) Historical risk 8Prepared by Alhaj Nuhu Abdulrahman Practical Illustration :

9. Solution 1) HPR = So HPR 1 = HPR 2 = HPR 3 = HPR 4 = HPR 5 = 2) AAR = 9Prepared by Alhaj Nuhu Abdulrahman

10. Solution 3) GAR = 1.134396475 – 1 = 0.1344 or 13.44% Or (1.878556848) 1/5 – 1 = (1.878556848) 0.2 – 1 = 13.44% 10Prepared by Alhaj Nuhu Abdulrahman

11. Solution 4) Historical risk σ 2 = = = 1,629.6 σ = = 40.37% This indicates high risk investment because the 40.37% standard deviation (risk level) is high. 11Prepared by Alhaj Nuhu Abdulrahman

12. The Capital Market Efficient Hypothesis The capital market efficient hypothesis is a term used to describe how stock prices adjust to the flow of any relevant information in an economy. Thus no individual market participant can use such information to make profit against the rest. The efficient market hypothesis suggests that security prices adjust rapidly and rationally to new information about the firm. The competition among participants, the rapid dissemination of information, and the swiftness with which security prices adjust to this information produce efficient stock market in which no participant can be a privy to a piece of information it can use to beat other competitors and make extra profits. This information has been classified into three types: (1) information on past prices, (2) information on management decisions or achievements and (3) all other information including insider ones. On the basis of the three classified information, three forms of efficient market hypotheses have been developed namely: weak-form efficient market, semi-strong-form efficient market and strong-form efficient market. 12Prepared by Alhaj Nuhu Abdulrahman

13. The Capital Market Efficient Hypothesis Weak-form efficient market: This hypothesis suggests that the current stock price fully reflects information on historical price movements. Thus, not beneficial to dealers and investors to analyse past price behaviour for forecasting future prices to beat the market and make profit solely on that. Semi-strong-form efficient market: This hypothesis suggests that stock price fully reflects all relevant publicly available information about the firm which include not only past price movements but also information on earnings, dividends, technological breakthrough, resignation of Directors, etc. It implies there is no advantage in analysing publicly available information because it is already absorbed into the price. Strong-form efficient market: This hypothesis states that the current stock price reflects all available public information as well as all privileged or insider information concerning the firm. Insider information refers to information about a firm currently known only to the firm’s Directors. Thus, even access to insider information cannot be used to make superior investment returns because it is illegal to abuse that privilege. 13Prepared by Alhaj Nuhu Abdulrahman

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