1 RETURN, RISK AND EQUILIBRIUM BY PROF. SANJAY SEHGAL DEPARTMENT OF FINANCIAL STUDIES UNIVERSITY OF...
-
Upload
denis-watkins -
Category
Documents
-
view
214 -
download
1
Transcript of 1 RETURN, RISK AND EQUILIBRIUM BY PROF. SANJAY SEHGAL DEPARTMENT OF FINANCIAL STUDIES UNIVERSITY OF...
1
RETURN, RISK AND EQUILIBRIUM
BY
PROF. SANJAY SEHGALDEPARTMENT OF FINANCIAL STUDIESUNIVERSITY OF DELHI SOUTH CAMPUS
NEW DELHI-110021
PH.: 0091-11-24111552Email: [email protected]
K2
2
PROMINENT INVESTMENT OBJECTIVES
• Regular income
• Income on Income
• Capital appreciation
• Safety of capital
• Liquidity
• Tax considerations
3
THE TWO PARAMETER FRAMEWORK
Maximize Expected Utility E(U) = f(Return, Risk)
Pre-conditions for the Two-parameter to work in financial markets
• Historical distribution of returns exhibit normality
• Investor utility functions are quadratic in nature, i.e.
E(U) f(mean, variance)
4
EX-ANTE RETURN AND RISK ON SECURITY i
Expected Return
E(Ri) = PiOi
Standard Deviation of return
i = Pi[Oi - E(Ri) ]2
Variance of returns
Var(Ri) = 2
5
AN EXAMPLE
Economic Probability Outcome (%) .
scenario Security 1 Security 2
Good 0.3 25 40
Average 0.5 20 10
Poor 0.2 15 - 10
E(R1) = .3 x 25 + .5 x 20 + .2 x 15 = 20.5%
E(R2) = .3 x 40 + .5 x 10 + .2 x -10 = 15%
1 = [.3(25 - 20.5)2 + .5(20 - 20.5)2 + .2(15 - 20.5)2]1/2 = 3.5%
2 = [.3(40 - 15)2 + .5(10 - 15)2 + .2(-10 - 15)2]1/2 = 18% approx.
6
EX-POST RETURN ON SECURITY i
One- period return
P1 – P0 D1
R1 = ----------- + ----------
P0 P0
Capital Dividend
gains Yield
yield
NOTE: 1. Ignoring dividend yield one can compute approximate one-period return as
P1 – P0
R1 = -----------
P0
2. The square of the period returns can be used to estimate average returns.
7
CAPITALISATION CHANGES AND STOCK PRICES
1. Stock Dividends
If a firm issues a stock dividend on n:m, then ex-stock dividend price = m/(n+m), where n = new share issued, m = old shares with shareholders.
Example: A firm issues tock dividend of 2:3, The ex-stock dividend price = 3/5.
2. Rights Issues nP1 + mP2
The ex-rights price of a firm = ---------------
n + m
where n = rights shares, m is old shares, n = issue price, m = last cum-rights selling price
Example: A firm offers a rights price is 2:3. The issue price is IOE, while the cum-rights selling price is 25 Euros.
2 x 10 + 3 x 25 95
Ex-rights price = -------------------- = ----- = 19 Euros
2 + 3 5
8
Ex-rights price 19
Rights adjustments factor = ------------------------------------- = ----
Last cum-rights selling price 30
3. Stock Splits
If a firm announces a stock split of n:m, ten ex-stock split price is n/m.
Example: If stock split is 1:10, then ex-stock split price is 1/10.
9
MEASURING AVERAGE RETURNS
Geometric average returns
Using one-period gross returns, we estimate Ex-post GM returns
RGM = [(1 + R1) (1 + R2) … (1 + RK)1/K] - 1
Arithmetic average returns
Using one period net return we estimate Ex-post arithmetic average returns as
w
E(R) or AM = Ri/N
i=1
Arithmetic average is preferred because
• Easier to compute• It has more desirable mathematical properties• A better proxy for forward looking returns.
10
ESTIMATING EX-POST RETURN: AN ILLUSTRATION
Months Monthly Return (1%)
1 6
2 2
3 4
E(Rt) = Ri/3 = 4%
6 + 2 + 4
1. Ex-post return based on arithmetic mean = ------------- = 4%
3
2. Ex-post return base don geometric mean = cube root of [(1.06) (1.02) (1.04)] – 1
= [(1.06) (1.02) (1.04)]1/3 – 1 =
11
EX-POST MEASURES OF RISK
Total risk measure standard deviation of returns
i = 1/N-1 (Ri - E(Ri))2
An Example
Months Monthly Return (1%)
1 6
2 2
3 4
E(Rt) = Ri/3 = 4%
i = ½ [(6 - 4)2 + (2 - 4)2 + (4 - 4)2]
= 2%
NOTE: Standard deviation as a risk measure assumes that historical returns follow a normal distribution
12
DECOMPOSING TOTAL RISK
Total Risk = systematic risk + unsystematic risk
2i = 2
i 2M + 2
ei
Systematic risk variations in stock returns is owing to shifts in common macro-economic factors.
Unsystematic risk: variation in stock returns is owing to micro-economic shocks.
• Unsystematic risk is diversifiable in a large portfolio.
• Sources of unsystematic risk
• Industry factors
• Group factors
• Common factors
• Firm specific factors.
BETA AS A MEASURE OF SYSTEMATIC RISK
• Beta measures the sensitivity of stock returns to market index returns.
• It is estimated as the slope of the regression of stock returns on market returns.
Rit = α + β RMt + eit
• Mathematically
Cov RiRM
β = ----------------
Var RM 13
STOCK CLASSIFICATION ON THE BASIS OF BETAS
β > 1 Aggressive stocks
β = 1 Average stocks
β < 1 but > 0 Defensive stocks
β = 0 Risk-free asset
β < 0 Hedging stocks
14
15
BETA AND STOCK CLASSIFICATION
Estimating Beta of a listed company - An Example
Problem
Month Return on Return on
security i (%) Market Index
1 10 12
2 6 5
3 13 18
4 -4 -8
5 13 10
6 14 7
7 4 15
8 18 30
9 24 25
10 22
Solution
Cov RiRM = .778
Var (RM) 1022
Cov RiRM
I = ------------- = 0.76
Var RM
Time Series Regression: Estimating Beta for HDFC Bank stock
Time Period: 2005-2007
Market Index : CNX S&P 500
The Model: Rit= a + bRmt
Output:
Rit = 0.142 + 0.704Rmt
(1.126) (3.393)
R2= 0.313
16
Regression Results using Excel: Estimating Beta for HDFC Bank stock
17
Regression StatisticsMultiple R 0.5598034R Square 0.3133798Adjusted R Square 0.2931851Standard Error 0.0670837Observations 36
ANOVA df SS MS F Significance F
Regression 1 0.069834096 0.07 15.52 0.00038525Residual 34 0.15300763 0.005Total 35 0.222841726
Coefficients Standard Error t Stat P-value Lower 95%Intercept 0.0142604 0.012654992 1.127 0.268 -0.01145766Rm 0.7040934 0.178736648 3.939 4E-04 0.340856844
18
PRECAUTIONS WHILE ESTIMATING BETA
• Number of observations: 48 - 60
• Observation frequency: monthly or weekly data
• Market index: broad-based and value-weighted
• Trading frequency: Active trading record.
UNLEVERED AND LEVERED BETAS
• Unlevered Beta is a measure of operating risk of the firm.
• Levered Beta is a measure of both operating and as well as financial risk of the firm.
βL = βU [1 + (1 – TC)] D/E
Or
βU = βL/[1 + (1 – TC)] D/E
19
THE RELATIONSHIP BETWEEN RISK AND RETURN
Estimating required returns: THE CAPITAL ASSET PRICING MODEL or CAPM approach
R(R) = RF + (ERM – RF) βi
Estimating expected returns: DIVIDEND CAPITALISATION MODEL APPROACH
D1 D1
P0 = ------------- or ER = ----- + g
ER – g P0
20
AN EXAMPLE
Risk-free rate of return = 10%
Return on market index = 14%
Beta of IBM stock = 1.25
Dividend paid last year by IBM = 1.70 E
Growth rate of IBM = 6%
Current price of IBM stock = 22E
Estimating R(R)
R(R) = 10 + (14 – 10) 1.25 = 15%
Estimating E(R)
1.70 (1.06)
E(R) = -------------- + .06 = 14.18%
22
Since, ER < RR, IBM stock is overvalued. This is a sell signal 21
Equilibrium Value of IBM stock
D1
Eqn. P0 = -------------
R (R) – g
1.80
= ----------- = 20 E
.15 - .06
Since P0 (22E) > Eqm. P0 (20E), the stock is overvalued. It is a sell signal.
22
23
CHANGE IN EQUILIBRIUM PRICE
Change in response to changes in underlying variables.
Variable Old Value Revised value
RF 10% 9%
ERM - RF 4% 3%
1.25 1.33
g 6% 8%
Revised R(R)
= 9 + 3 (1.33) = 13%
1.70 (1.08)
Eqm Price = --------------
.13 - .08
= 36.80 E