Download Expected Return Standard Deviation

Presentation 3: Objectives
To introduce you with the Principles of
Investment Strategy for asset allocation and
Modern Portfolio Theory
Topics to be covered
 Capital Allocation Line, Sharpe Ratio,
Optimal Portfolio, Capital Market Line, CAPM,
APT, EMH
1
Background
Return
Efficient
Risk
Capital Allocation Line
rf
rf
p
E(rp)
y = % in p
(1-y) = % in rf
 C  y P
6-3
E ( rc )  r f  y  E ( rP )  r f 
Capital Allocation Line
Rearrange and substitute y=C/P:
C

E rC   rf 
E rP   rf 
P
Slope 
Sharpe Ratio
6-4
E rP   rf
P
Risk Tolerance and Asset
Allocation
2
1
Max U  E (rc ) 
A C
2
2 2
1
 rf  y[ E (rp )  rf ] 
Ay  p
2
y 
*
E (rp )  rf
A
2
p
Risk Tolerance and Asset
Allocation
 Investor’s risk aversion level =3.
 Fund manager A
 E(R): 9%
 SD: 15%.
 Fund manager B
 E(R): 18%
 SD: 25%.
y 
*
E (rp )  rf
A
2
p
 T-bill : 6%
 What is the optimal position these two fund manager should
take for this investor (if this investor becomes one of their
clients)?
Optimal Risky Portfolio with
a Risk Free Asset
Example
In risky portfolio – we have stocks and
bond
Now we include a risk free asset giving a
return of 3%
Optimal Risky Portfolio with
a Risk Free Asset
ER(%)
ER(%)
Optimal Risky Portfolio with
a Risk Free Asset
31.24%
45.00%
Bond
Stock
Tbill
23.76%
Efficient Diversification with three
risky assets
Expected Return
0.25
C
0.2
0.15
B
0.1
A
0.05
0
0
0.05
0.1
0.15
0.2
0.25
Standard Deviation
3 assets portfolio
0.3
0.35
Efficient Diversification with three
risky assets
0.25
Expected Return
0.2
C
0.15
B
1&2
0.1
1&3
2&3
A
Mixed
0.05
0
 3 assets portfolio
0
0.05
0.1
0.15
0.2
Standard Deviation
0.25
0.3
0.35
Efficient Diversification with many
risky assets
Capital Market Line
p

E rp   rf 
E rm   rf 
m
Short Selling
Capital Market Line
Separation Theorem
James Tobin (1958) paper said if you hold
risky securities and are able to borrow buying stocks on margin - or lend - buying
risk-free assets - and you do so at the
same rate, then the efficient frontier is a
single portfolio of risky securities plus
borrowing and lending…
Capital Market Line
Tobin's Separation Theorem separate the
problem into :
first finding that optimal combination of
risky securities
deciding whether to lend or borrow,
depending on your attitude toward risk.
if there's only one portfolio plus borrowing
and lending, it's got to be the market.
Expected Return
Capital Market Line
M
Rf
m
Standard Deviation
Expected Return
Capital Market Line
.
A
.
M
.
CML
B
Rf
Standard Deviation
Capital Market Line
E R p   X 1 R1  X 2 R2
  X   X   2 X1 X 21 2 12
2
p
2
1
2
1
2
2
2
2
  X   X   2 X1 X 21 2 12
2
p
2
1
2
1
 p  X1 1
2
2
2
2
Capital Market Line
Tobin's Separation Theorem separate the
problem into :
first finding that optimal combination of
risky securities
deciding whether to lend or borrow,
depending on your attitude toward risk.
if there's only one portfolio plus borrowing
and lending, it's got to be the market.
CAPM
William F. Sharpe
Sharpe, W. (1964) A Theory of the Market
Equilibrium under conditions of Risk, Journal of
Finance, 19, 425-442
Noble Prize in Economics 1990
google image
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CAPM
Treynor, J. (1961) Toward a Theory of Market Value
of Risky Assets, unpublished manuscript.
 J. Lintner (1965) The valuation of Risk Assets and
the Selection of Risky Investments in Stock Portfolios
and Capital Budgets, Review of Economics and
Statistics 47, 13-37
 J. Mossin (1966) Equilibrium in a Capital Asset
Market” Econometrica, 34, 768-783
21
CAPM Assumptions
Investors rely on two factors in making their
decisions: expected _ _ _ _ _ _ and variance.
Investors are rational and risk a_ _ _ _ _ and
subscribe to Markowitz (1958) methods of portfolio
diversification.
Investors all invest for the same period of time.
There is a risk _ _ _ _ investment, and investors can
borrow and lend any amount at the risk-free rate.
Capital markets are completely competitive
22
CAPM Terminologies: Systematic and
Unsystematic risk
In the development of portfolio theory
Markowitz (1958) defined the variance of the
rate of return as the appropriate measure of
risk.
However this can be sub-divided into two
general types of risk: systematic and
unsystematic risk.
William Sharpe (1963) defined systematic risk as
the portion of an assets variability that can be
attributed to a common factor.
Systematic (or market risk) is the minimum level
of risk
23
CAPM Terminologies: Systematic and
Unsystematic risk
Sharpe (1963) defined the portion of an assets
variability that can be diversified away as
unsystematic (or unique) risk.
24
CAPM Terminologies: Systematic and
Unsystematic risk
Total Risk:
Systematic + Unsystematic
25
CAPM Terminologies: Systematic
and Unsystematic risk
Select from the following as cause for
systematic and Unsystematic Risks :
Inflation
Announcement of a small oil strike by a
company
Government Tax Policy
Recession
Decision of management of the company to
expand/ contract
26
CAPM Terminologies: Systematic and
Unsystematic risk
AKA (Systematic or Unsystematic?)
Diversifiable risk
Asset specific risks
Market risks
Unique risk
Controllable
Idiosyncratic risk
Uncontrollable
Portfolio risk
27
Standard Deviation of Return
CAPM Terminologies: Systematic and
Unsystematic risk
Even a little
diversification can
substantially reduce
variability. Unsystematic
Risk can be reduced by
diversification
Total
Risk
Unique risk
Systematic Risk
Standard Deviation of the
Market Portfolio (systematic
risk)
Market risk
Number of Stocks in the Portfolio
Expected Return on Individual
security (using CAPM)
The b is the covariance between the return of
a security and the market return divided by the
variance of the market return.
Covariance (R , R )
β
Variance (R )
i
m
m
It is a stock’s sensitivity to changes in the
value of the market portfolio
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Expected Return on Individual
security (using CAPM):
If an investor wants to avoid risk altogether, he
must invest in a portfolio consisting entirely of
………………………. such as ……………………..
30
Expected Return on Individual
security (using CAPM):
 If an investor wants to avoid risk altogether, he must invest
in a portfolio consisting entirely of risk free securities such
as Government Debt
 If the investor holds only an undiversified portfolio of
shares he will suffer unsystematic risk as well as systematic
risk.
 If an investor holds a ‘balanced portfolio’ of all the stocks
and shares on the stock market, he will suffer risk which is
the same as the average systematic risk in the market.
 Individual shares will have risk characteristics which are
different to this market average.
 Their risk will be determined by the industry sector and
gearing. Some shares will be more risky and some less.
31
Expected Return on Individual
security (using CAPM)
 The market portfolio (remember, this is the portfolio of
all the shares in the market weighted by capitalization)
is taken to be the benchmark and is given a β factor of
1.
 All other shares or portfolios will have a β factor greater
or smaller than 1 depending on their systematic risk
which is measured by considering their required returns.
If a share or portfolio has a β factor of 0.5 it will move
in line with the market movements but only half as
much. If the share or portfolio has a β factor of 2, it will
again move in line with the market but twice as much.
32
Expected Return on Individual
security (using CAPM)
If a stock has the same risk as the whole
market portfolio then, B = ……..
If asset is less risky than the whole
market portfolio then Beta = ………
If asset is more risky than the whole
market portfolio then Beta = ……..
33
Expected Return on Individual
security (using CAPM)
Shares classified by their betas are
described by some writers as aggressive,
defensive or Neutral
 b = 1, > 1, < 1
34
CAPM: The Security Market Line
(SML)
 Shows the relationship between the return of a equity
and the β of the equity
Expected Return
SML
Rm
Rf
b1
 Higher b means higher risk premium
35
CAPM: The Security Market Line
(SML)
 Suppose Rf is 6 %, Rm is 10% and if b = 1 then
 Return on equity (also, Cost of equity) =
R i  R RF  β (R M  R RF )
 = 6% + 1 x (10% - 6%)
 = 10%
 Now suppose the b is 0.5 then
 = 6% + 0.5 x (10% - 6%)
 = 8%
 Again if b = 2
 = 14%
36
CAPM: The Security Market Line
(SML)
SML then will be
SML
Expected Return
14%
10%
8%
6%
b  0.5
b1
b2
37
EMH
19th Sept :$ 93.89
14th Oct :$ 84.95
28th Oct :$ 99.68
21/10/2014
22/10/2014
23/10/2014
24/10/2014
27/10/2014
28/10/2014
90.9
91.63
94.45
95.76
97.79
99.68
38
EMH
“Don’t bother if the bill were real
someone would have picked it
up already”
Markets are generally very
efficient but rewards to the
especially - diligent, Intelligent,
Creative may in fact be waiting
Random Walks
 "The Theory of Speculation”
 Random Walk – 114 Years
Karl Pearson (1905), walk of
drunk, Nature.
Louis Bachelier
Burton Malkiel,
1973.
A Random Walk Down Wall Street,
Market is Irrational
Kendall and Hill (1953)
Stock Price -No logical rules
Erratic Market Psychology AKA “Animal
Spirits”
Prices seems to evolve randomly -Market
is Irrational
Random Walks
Coin Toss Game
Head
Head
£106.09
£103.00
£100.43
Tail
£100.00
Head
£100.43
£97.50
Tail
£95.06
Tail
Informational Efficiency Efficient Markets Hypothesis (EMH)
Fama (1970) - identified three classifications of
efficiency:Weak form - prices reflect all _ _ _ _information.
Semi-strong form - prices reflect all past and _ _ _ _
_ _ _ publicly available information.
Strong form - prices reflect all public AND _ _ _ _ _ _
_ information - may include privileged (_ _ _ _ _ _ )
information.
Empirical evidence suggests all major stock
markets are at least _ _ _ _ form efficient.
43
Efficient Markets Hypothesis (EMH)
Implications of 3 forms
 An implication of weak form efficiency is that investors
cannot out-predict the market when they predict returns
using models based on _ _ _ _ _ _ _ _ _ _ prices.
 An implication of semi-strong form efficiency is that
when a public announcement is made which is relevant
for a security, the price of that security should
immediately _ _ _ _ to its equilibrium level.
 An implication of strong-form efficiency is that investors
can _ _ _ earn extra returns, even when they use their
own private information to forecast future returns and
prices.
44
EMH - example
 Company X has 1 m shares and a market value of
£3million.
 On 1/12/2013 it considers a project which will cost
£2million and yield cash flows of £0.5million per
year forever.
 The discount rate is 20%.
 On 4/12/2013 the board disclose details of the
project to the market but do not mention additional
redundancy costs of £0.4million.
 On 10/12/2013 all relevant information is released
to the market.
45
EMH - example
Opening Share Price : = …………per share
Semi-Strong form efficiency:
1/12/2013 : _ _ change as no info is made
public.
4/12/2013 : NPV of project = ………………
Share Price = …………….
10/12/13 : All information is made public.
Share Price = ………………
46
EMH - example
Strong Form efficiency:
Provided all financial implications were
known on 1/12/2013 the share price would
immediately go to ………….
Final price is the same but speed of
adjustment is quicker.
47
Event Studies
Read the news
5th January 2009
 Read the news : Fortunately, after further
testing, my doctors think they have found
the cause—a hormone imbalance that has
been “robbing” me of the proteins my
body needs to be healthy. Sophisticated
blood tests have confirmed this diagnosis.
48