1. 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

2. The Art of Investment is a Combination of Psychology & Statistics

3. Psychology Human Weaknesses Self-analysis Patience Adventurous
Pressure

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

5. 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 
Probability
From the principle of expected value, the expected price change in
Stock A (in one week)
= $[2 × (1) × × (+ 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.

6. Difference between Investment and Gambling

7. 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
=-$16.67 X 500
= -$

8. 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 = $

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

10. 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

11. 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

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

13. Avoiding Bankruptcy Companies
Z = 1.2X X X3 + X X5
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.

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

15. 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

18. 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

19. 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

21. Derived Securities
Future
Option: Call and Put