Transcript 投影片 1 - 培生香港

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
5500
1996
1997
1998
1999
2000
5000
Greedy
4500
4000
3500
3000
NASDAQ Index
2500
2000
1500
1000
500
Source: Bloomberg，Jan 1, 1996 to Apr 30, 2001
Afraid
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
.40
.20
.10
.1
0.20
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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Pay
$300
$600
$1200
$300
$600
$1200
$300
$300
$600
$300
$600
Win/Loss
L
L
W
L
L
W
W
L
W
L
W
Cash
-$300
-$900
$300
0
-$600
$600
$900
$600
$1200
$900
$1500
Expected Value for 500 games = $300 X 17/36 X 500 = $70833.33
Risk of 3 Dice Game
Pay
1. $300
2. $600
3. $1200
4. $2400
5. $4800
6. $9600
7. $19200
8. $38400
9. $76800
10. $153600
11. $307200
Gain/Loss
L
L
L
L
L
L
L
L
L
L
L
Cash
-$300
-$900
-$2100
-$4500
-$9300
-$18900
-$38100
-$76500
-$153300
-$306900
-$614100
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+BX
A: Alpha value
B: Beta value
Y: portfolio`s return
X: market`s return
Standard Deviation
 
n

Ri
i 1
 ER 
n 1
2
 = standard deviation of single asset
P 
n
n
CovijWiW j
i 1 j 1
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
b = base
Y = exponent
equal to by = X
What is log?
X
1
2
4
8
16
32
Log2 X
0
1
2
3
4
5
20=1
21=2
22=4
23=8
24=16
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
nΣx2 - (Σx)2
Moving Average
n
• MA(t,n) =  P(t-k+1) /n
k=1
• MA(t,n): n day moving average on period t
• P(t): price on period t
Derived Securities
• Future
• Option: Call and Put