Dr Chan Yan Chong 曾淵滄博士 City University of Hong Kong Investment and Decision Making: Everything is Mathematics? 投資與決策 ──  一切皆數? Dr Chan Yan Chong 曾淵滄博士 City University of Hong Kong

The Art of Investment is a Combination of Psychology & Statistics

Psychology Human Weaknesses Self-analysis Patience Adventurous Pressure

Emotion of Investors Greedy NASDAQ Index Afraid Source: Bloomberg，Jan 1, 1996 to Apr 30, 2001

An investor wants to make a week basis investment on Stock A with the information below. Price change of Stock A after one week ($)  2  1 0 +1 +2 Probability 0.20 .40 .20 .10 .1 From the principle of expected value, the expected price change in Stock A (in one week) = $[2 × 0.2 + (1) × 0.4 + 0 × 0.2 + (+ 1) × 0.1 + (+ 2) × 0.1] =  $ 0.5 A negative expected price change indicates that the price of Stock A is likely to decrease after one week. In other words, the investor is likely to lose money if he makes the investment on Stock A.

Difference between Investment and Gambling

3 Dice Game Probability of BIG or SMALL = 1/2 - 1/36 = 17/36 Expected Value for $300 game = $300 X 17/36 - $300 X 19/36 = -$16.67 Expected Value for 500 $300 games =-$16.67 X 500 = -$8333.30

3 Dice Game Pay Win/Loss Cash 1. $300 L -$300 2. $600 L -$900 Expected Value for 500 games = $300 X 17/36 X 500 = $70833.33

Risk of 3 Dice Game Pay Gain/Loss Cash 1. $300 L -$300 2. $600 L -$900

Assessing Risk Risk has many connotations. In the field of investment, the concept of risk has slowly changed over many years. Early 1900: Risk is debt and variability of net asset value Markowitz(1952): Risk is the beta value of CPAM Sharp(1981): Risk is the variability of rate of return which can be measured by standard deviation

Beta Value: CAPM CAPM: Capital Asset Pricing Model Y = A + B X A: Alpha value B: Beta value Y: portfolio`s return X: market`s return

Standard Deviation  = standard deviation of single asset p : standard deviation of a portfolio Wi : weight of stock i in the portfolio

Avoiding Bankruptcy Companies Z = 1.2X1 + 1.4X2 + 3.3X3 + X4 + 0.6X5 X1: working capital / assets X2: retained earnings / assets X3: pretax earnings / assets X4: sales / assets X5: market value of equities / liabilities If Z < 1.81 is classified as troubled.

How to use logarithm (log) application for analyzing stock market tendency？ Y = logb X equal to by = X b = base Y = exponent

What is log? X Log2 X 1 20=1 2 21=2 4 22=4 8 3 23=8 16 24=16 32 5 25=32

Linear Regression Line How this method is used to analyze the stock market tendency and the cycle? y = a+bx b = nΣxy – ΣxΣy nΣx2 - (Σx)2 a = Σx2Σy - ΣxΣxy

Moving Average MA(t,n) =  P(t-k+1) /n MA(t,n): n day moving average on period t P(t): price on period t

Derived Securities Future Option: Call and Put