Module 1 Investment Policy and Modern Portfolio Theory

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Module 1Investment Policy and Modern Portfolio
Theory
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Portfolio construction

• Purpose maximization of wealth by reaching a
  heuristic Reward-to-risk
• How? Allocate, Select and Protect
• Illustration realized and expected wealth?
• Realized wealth Expected wealth
  Error
• Heuristic Reward to risk Allocation
  Selection protection
• It always starts with the Policy
• Ask the right question!? what risk? ?Thus, what
  allocation?
• Set the right allocation target in terms of
  objectives, constraints and weight range
  monitoring

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Choose a Portfolio strategy Passive or Active
Asset allocation Security Selection
Active (for pros) Market timing Stock/Bond picking
Passive (for ind.) Fixed weights Indexing

• No matter what, an investment strategy is based
  on four decisions
• What asset classes to consider for investment
• What normal or policy weights to assign to each
  eligible class
• The allowable allocation ranges based on policy
  weights
• What specific securities to purchase for the
  portfolio
• Most (85 to 95) of the overall investment
  return is due to the first two decisions, not the
  selection of individual investments

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First, set the rules the policy statement

• TOTAL RETURN INCOME YIELD CAPITAL GAIN YIELD
• Objectives Think in terms of risk and return to
  find the best weightsi.e.,
• Capital preservation (high income, low capital
  gain)? Low to moderate risk
• Balanced return (Balanced capital gains and
  income reinvestment)?moderate to high risk
• Pure Capital appreciation (high capital gains,
  low to no income)?High risk
• Constraints - liquidity, time horizon, tax
  factors, legal and regulatory constraints, and
  unique needs and preferences
• Management - Define an allowable allocation
  ranges based on policy weights
• Selection - Define guideline to pick securities
  to purchase for the portfolio (optional)

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Examples of Investment Styles
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Objectives ?Age/Risk Matrix
Risk tolerance/ Time Horizon 0-5years (C/B/S) 6-10 (C/B/S) 11 (C/B/S)
Higher 10/30/60 0/20/80 0/0/100
Moderate 20/40/40 10/40/50 10/30/60
Lower 50/40/10 30/40/30 10/50/40

• C stands for CASHi.e. money market securities
• B stands for Bondsi.e. corporate, municipal or
  treasury securities
• S stands for Stocksi.e. value, growth,
  international equity securities
• Color code
• Capital preservation
• Balanced return
• Capital appreciation

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YOUR TURN!

• Mr. Bob is 70 years of age, is in excellent
  health pursues a simple but active lifestyle, and
  has no children. He has interest in a private
  company for 90 million and has decided that a
  medical research foundation will receive half the
  proceeds now it will also be the primary
  beneficiary of his estate upon his death. Mr. Bob
  is committed to the foundation s well-being
  because he believes strongly that , through it, a
  cure will be found for the disease that killed
  his wife. He now realizes that an appropriate
  investment policy and asset allocation are
  required if his goals are to be met through
  investment of his considerable assets. Currently
  the following assets are available for building
  an appropriate portfolio
• 45 million Cash (from the sale of the private
  company interest, net of 45 million gift to the
  foundation)
• 10 million stocks and bonds (5 million each)
• 9 million warehouse property not fully leased)
• 1 Million Bob residence
• Build a policy statement for Mr. Bob!

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Objectives (return)

• Large liquid wealth from selling interest in the
  private company
• Income from leasing warehouse
• Not burdened by large or specific needs for
  current income nor liquidity.
• He has enough spendable income.
• He will leave his estate to a Tax-exempted
  foundation
• He has already offered a large gift to the
  foundation
• Thus, an inflation-adjusted enhancement of the
  capital base for the benefit of the foundation
  will the primary minimum return goal.
• He is in the highest tax bracket (not mentioned
  but apparent)
• Tax minimization should be a collateral goal.

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Objectives (risk)

• Unmarried, Childless, 70 years old but in good
  health
• ? Still a long actuarial life (10), thus long
  term return goal.
• Likely free of debt (not mentioned, but neither
  the opposite)
• Not skilled in the management of a large
  portfolio
• Yet, not a complete novice since he owned stocks
  and bonds prior to his wifes death.
• His heirthe foundationhas already received a
  large asset base.
• ?Long term return goal with a portfolio bearing
  above average risk.

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Constraints

• Time--Two things (1) long actuarial life and (2)
  beneficiary of his estatethe foundation has a
  virtually perpetual life
• Taxes highest tax brackets, investment should
  take this into consideration tax-sheltered
  investments.
• Unique circumstances Large asset base, a
  foundation as a unique recipient? some freedom in
  the building of the portfolio

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Adapted Strategy

• Majority in stocks (shield against inflation,
  above average risk tolerance, and no real income
  or liquidity needs)
• He already has 15 in real estate (house
  warehouse)? no more needed, diversification
  effect achieved.
• Additional freedom Non-US stocks? additional
  diversification
• ? Target 75 equity (including Real Estate)
• Fixed Income used to minimize income taxesi.e.,
  municipal and treasury securities. No need to
  look for YIELD nor downgrade the quality of the
  issues used.
• Additional freedom Non-US fixed-income?
  additional diversification effect.
• ? Target 25 in fixed income

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Proposed Allocation
Current Proposed Range
Cash / Money Market 70 0 0-5
US Stocks--LC 30 30-40
US StocksSC 15 15-25
Non US Stocks 15 15-25
Total 7.5? 60 60-80
Real Estate 15 15 10-15
US Fixed Income 15 10-20
Non-US Fixed Income 10 5-15
Total Fixed Income 7.5? 25 15-35
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In sum, the Importance of Asset Allocation

• An investment strategy is based on four decisions
• What asset classes to consider for investment
• What normal or policy weights to assign to each
  eligible class
• The allowable allocation ranges based on policy
  weights
• What specific securities to purchase for the
  portfolio
• Most (85 to 95) of the overall investment
  return is due to the first two decisions, not the
  selection of individual investments
• Summary
• Policy statement determines types of assets to
  include in portfolio
• Asset allocation determines portfolio return more
  than stock selection
• Over long time periods sizable allocation to
  equity will improve results
• Risk of a strategy depends on the investors
  goals and time horizon

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What is Investments?

• Purpose maximization of portfolio wealth through
  adequate Portfolio management
• Fair Reward-to-risk? Ask the right question!
• Optimal portfolio management
• Allocation Selection Risk protection

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Investment Vehicles

• Investments divided by asset class.
• 1. Fixed-income investments (MM 27 Bonds 49)
• 2. Equity investments (stocks 140, COM.)
• 3. Derivatives (Options and futures)
• 4. Investment companies (MF 106, HF)
• 5. Real estate
• 6. Low-liquidity investments

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Build a general culture on investments (Risk,
Returns, Correlations)

• US asset classes
• Security markets size
• Government bond return
• Global equity returns
• Correlations
• Global Asset classes performance/correlation
• Investment companies performance

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Alternative InvestmentsRisk and Return
Characteristics
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Computing Returns

• The additional cents on the dollar invested
• R(profitadditional cash flows)/initial
  investment
• Over a period of timeaverage return
• Average returnS(all returns)/nb of observations
• Why do returns matter?
• does not mean muchalone
• Cross-comparison between markets
• Are normally distributed

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Example 1 Market Order

• You buy a round lot (multiple of 100) of ABC
  stock at 20. Brokerage fees are 3 on each
  transaction (3 for purchase and 3 for sale).
  You receive a year later 0.5 per share in
  dividends and sell the stock at 27. What is the
  rate of return on investment?
• Market Orders - buy or sell the stock at the best
  price at that time.

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Solution 1

• RProfit/investment
• Return Profit/initial investment
• (Ending value - Beginning Value Dividends -
  Transaction costs on purchasing and selling) /
  (initial investment transaction costs on
  purchasing)
• Beginning Value of Investment 20n
• Ending Value of Investment 27n
• ?Dividends 0.5n
• ?Transaction Costs for purchase3 x 20n0.6n
• ?Transaction Costs for sale3 x 27n0.81n
• Profit 27n - 20n 0.5n-0.6n-0.81n 6.09n
• Initial investment 20n0.6n 20.6n
• R 6.09n/20.6n 6.09/20.6 29.56

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Example 2 Stop loss orders

• Suppose you have 500 shares of ABC stock, bought
  at 50 and priced at 60. You put a stop loss
  order at 55. Why would you do that? If the the
  price goes to 52, what would be your rate of
  return with and without the stop loss order?
• Special orders
• Stop loss order Implies that if the market price
  falls to or below a specified price, the order
  becomes a market order and the stock will be sold
  at the prevailing price.
  
  
  
  
  
  
• Stop buy order Used by short sellers to
  minimize losses if market price rises.
• Solution 2
• You are obviously satisfy with a profit of 5 per
  share.
• With stop loss R (55-50)/5010
• Without stop loss R (52-50)/504

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Example 3 Limit orders

• Xyz stock is selling for 40. You have a limit
  buy order at 35. During the year the stock goes
  to 30 then goes to 45. (1)What is R? (2)What
  would have R been with a simple market order?
  (3)What would R been is the limit buy order was
  at 25?
• Limit Orders - customer specifies highest
  purchase or lowest sell price. (Time
  specifications for order may vary Instantaneous
  - fill or kill, part of a day, a full day,
  several days, a week, a month, or good until
  canceled GTC)
• - limit buy specifies the highest price
  investor is willing to pay.
• - limit sell specifies the lowest price
  investor is willing to accept.
• Solution 3
• (1) When market declined to 30, your limit
  order was executed 35 (buy), then the price went
  to 45.
• Rate of return (45 - 35)/35 28.6.
•  (2)Assuming market order _at_ 40 Buy at 40,
  price goes to 45? Rate of return (45 -
  40)/40 12.5 .
•  (3) Limit order _at_ 25 Since the market did not
  decline to 25 (lowest price was 30) the limit
  order was never executed.

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Example 4 Margin Transactions

• Buy 200 shares at 50 10,000 position
• Borrow 50, investment of 5,000
• If price increases to 60, position
• Value is 12,000
• Less - 5,000 borrowed
• Leaves 7,000 equity for a
• 7,000/12,000 58 equity position
• Return on investment?
• Rprofit/initial investment(12000-10000)/500040

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Example 5 Margin Transactions

• Buy 200 shares at 50 10,000 position
• Borrow 50, investment of 5,000
• If price decreases to 40, position
• Value is 8,000
• Less - 5,000 borrowed
• Leaves 3,000 equity for a
• 3,000/8,000 37.5 equity position
• Return on investment?
• Rprofit/initial investment(8000-10000)/5000-40
  

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Example 6 Margin Transactions

• In the previous example, how far can the stock
  price fall, before you receive a margin call?
  Assume a maintenance margin of 25
• A call occurs when the proportion of equity
  minimum maintenance margin,i.e.
• 25(200P-5000)/200P
• So P5000/(200-25 x 200) 33.33

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Example 7 margin transactions

• You buy a round lot (multiple of 100) of ABC
  stock at 20 on 55 margin. The broker charges
  10 on the borrowed money Brokerage fees are 3
  on each transaction (3 for purchase and 3 for
  sale). You receive a year later 0.5 per share in
  dividends and sell the stock at 27. What is the
  rate of return on investment?

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Solution 7

• RProfit/investment
• Return Profit/initial investment
• (Ending value - Beginning Value Dividends -
  Transaction costs on purchasing and selling -
  interests paid on borrowed money) / (initial
  investment transaction costs on purchasing)
• Beginning Value of Investment 20n
• Ending Value of Investment 27n
• ?Dividends 0.5n
• ?Transaction Costs for purchase3 x 20n0.6n
• ?Transaction Costs for sale3 x 27n0.81n
• ?Interests on amount borrowed 10 x 45 x 20n
  0.9n
• Profit 27n - 20n 0.5n-0.6n-0.81n-0.9n
  5.19n
• Initial investment 55 x 20n0.6n 11.6n
• R 5.19n/11.6n 5.19/11.6 44.74

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Short sale example 8

• You sell short 200 shares of ABC, which is priced
  at 120. The margin requirement is 40.
  Commissions on sale are 113. During the year,
  dividends of 2.9 are paid. At the end of the
  year you repurchase the stock at 90 (you close
  your position!) and you are charged 109 plus 10
  on the money borrowed.
• What is you return on investment?

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Solution 8

• RProfit/investment
• Profit on a Short Sale Beginning Value -
  Ending Value- Dividends - Transaction Costs -
  Interest
• Beginning Value of Investment 200 x 120 shares
  24,000(which is sold under a short sale
  arrangement)
•   Ending Value of Investment 200 x 90
  18,000 (Cost of closing out position)
• ?Dividends 2.9 x 200 shares 580
• ?Transaction Costs 113 109 222
• ?Interest .1 x (.6 x 24000) 1,440
• Profit 24,000 - 18,000 - 580 - 222 - 1440
  3,758
• Your investment margin requirement commission
• (.40 x 24,000) 113 9600 113 9,713
• R 3,758/9,713 38.69

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Example 9 Computation of the Expected Return for
Risky Assets
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Risk

• We need to think in terms of estimates in an
  uncertain world
• Estimateaverage return /- some volatility
• Uncertainty or volatility of returns
• Standard deviation of returns
• Measured in
• What does it mean?

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Example 10 Risk

• Computation of Monthly Rates of Return

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Variance (Standard Deviation) of Returns for an
Individual Investment
Standard deviation is the square root of the
variance Variance is a measure of the variation
of possible rates of return Ri, from the expected
rate of return E(Ri)

• where Pi is the probability of the possible rate
  of return, Ri

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Example 11 Variance (Standard Deviation) of
Returns for an Individual Investment
Variance ( 2) .00050 Standard Deviation (
) .02236
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Example 12

• What is the probability for long-term government
  bonds to return more than 0?
• Z(5.6-0)/9.20.61?P72.9
• What is the probability to make more than 10
  with small caps?
• Z(17.7-10)/33.90.23?P59.1

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Risk and Return

• How to compare assets?
• Coefficient of variation measure of relative
  risk
• CV Total risk/return
• CS 1.56
• SCS 1.91
• CB 1.41
• TB 1.64
• Rf 0.84
• Which one do you pick?
• What is the problem here?

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Covariance of Returns

• A measure of the degree to which two variables
  move together relative to their individual mean
  values over time
• For two assets, i and j, the covariance of rates
  of return is defined as
• Covij ERi - E(Ri)Rj - E(Rj)

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Covariance and Correlation

• The correlation coefficient is obtained by
  standardizing (dividing) the covariance by the
  product of the individual standard deviations

• Correlation coefficient varies from -1 to 1

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Portfolio effect

• Portfolio Return is the weighted average return
  of each asset in the portfolio
• Portfolio Risk is not the weighted average risk
  of each asset in the portfolio. Portfolio risk
  has to do with each assets weight and risk, but
  also the degree to which they move together
  (corr)

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Mathematical Explanation
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Summary Portfolio effect

• Portfolio return (RP)
• Average return of all securities
• Portfolio risk (sP)
• Average risk of all securities
• Minus
• the propensity of those securities to be
  unrelated (returnwise!)

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Portfolio risk and returnin English

• Portfolio return
• (weighted) average assets return
• Portfolio risk
• (weighted) average assets risk
• (weighted) average assets prices propensity to
  move in opposite direction
• Or
• Portfolio risk
• (weighted) average assets risk
• - Benefits from diversification

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Combining Stocks with Different Returns and Risk

• Assets may differ in expected rates of return and
  individual standard deviations
• Negative correlation reduces portfolio risk
• Combining two assets with -1.0 correlation
  reduces the portfolio standard deviation to zero
  only when individual standard deviations are equal

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Example 13
1 .10 .07 2
.20 .1
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Portfolio Risk-Return Plots for Different Weights
E(R)
2
With two perfectly correlated assets, it is only
possible to create a two asset portfolio with
risk-return along a line between either single
asset
Rij 1.00
1
Standard Deviation of Return
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Portfolio Risk-Return Plots for Different Weights
E(R)
f
2
g
With uncorrelated assets it is possible to create
a two asset portfolio with lower risk than either
single asset
h
i
j
Rij 1.00
k
1
Rij 0.00
Standard Deviation of Return
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Portfolio Risk-Return Plots for Different Weights
E(R)
f
2
g
With correlated assets it is possible to create a
two asset portfolio between the first two curves
h
i
j
Rij 1.00
Rij 0.50
k
1
Rij 0.00
Standard Deviation of Return
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Portfolio Risk-Return Plots for Different Weights
E(R)
With negatively correlated assets it is
possible to create a two asset portfolio with
much lower risk than either single asset
Rij -0.50
f
2
g
h
i
j
Rij 1.00
Rij 0.50
k
1
Rij 0.00
Standard Deviation of Return
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Portfolio Risk-Return Plots for Different Weights
Exhibit 7.13
E(R)
f
Rij -0.50
Rij -1.00
2
g
h
i
j
Rij 1.00
Rij 0.50
k
1
Rij 0.00
With perfectly negatively correlated assets it is
possible to create a two asset portfolio with
almost no risk
Standard Deviation of Return
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Numerous Portfolio Combinations of Available
Assets
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Efficient Frontier for Alternative Portfolios
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Efficient Frontier In Practice (all equity
markets of the world 1981-2001)
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9 different Institutional efficient Benchmarks
Asset Allocation and cultural Differences

• Mindset, Social, political, and tax environments
• U.S. institutional investors average 45
  allocation in equities
• In the United Kingdom, equities make up 72 of
  assets
• In Germany, equities are 11
• In Japan, equities are 24 of assets

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Conclusion What is the use of an efficient set?

• Goal find an optimal mix (weight) so that the
  ratio of compensation for risk to risk (or reward
  to risk) is optimal for your level of risk
  tolerance.
• Your inputs Expected returns, standard
  deviations and correlations (for each asset
  class)
• Your output Optimal weight in each asset class
  (how much should you put in each asst class?)

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Can we do better than the efficient set?

• Imagine two portfolio (1) a risky best of the
  best portfolio with an expected return of Rm and
  a standard deviation of sm and (2) a riskless
  portfolio of t-bills with an expected of Rf and a
  standard deviation close to zero.
• You allocate Wrf in the riskless portfolio and
  (1-Wrf) in the risky (best of the best portfolio)
• The standard deviation and expected return of
  this portfolio shall be
• sp(1-Wrf) x sm or Wrf1- sp/sm, then
• RpWrf x Rf (1-Wrf) x Rp replace Wrf by 1-
  sp/sm
• RP Rf (Rm Rf) /sm x sp?Capital Market
  Line (CML)
• Rp intercept slope x sp

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What does it mean?
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It means that

• We know how to get the composition of the
  best-of-the-best portfolio (M)? It has the
  highest reward to risk i.e., (Rm Rf)/sm
• Then, we know how to get Rm and sm
• Finally, for the risk we are willing to take
  (indifference curve? policy statement), we can
  find our optimal asset allocation by mixing the
  best of the best portfolio with cash!
• Cool (I mean sweeeeet) huh?
• Application efficient frontier analysis

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Example 14

• Describe step by step how to build an efficient
  set and choose a portfolio that fits your risk
  tolerance.

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The selection process Risk and Diversification

• Return expected unexpected
• Risk (return) 0 market risk business risk
• The trick if you hold many securities, the
  particularities of each security becomes
  irrelevantthus, in a well diversified portfolio
  business-specific risk is irrelevant!

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Risk and Return

• The higher the risk, the greater the expected
  return.
• RiReal rate Inflation premium Risk premium
• Ririsk free rate compensation for risk
• Compensation for riskrisk premiumcompensation
  for a high standard deviation

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Risk that matters

• If only market risk matters, then the risk
  premium of a security should be related (somehow)
  to the market risk premium!
• Lets assume that those risk premiums are
  proportional
• security risk premiumß x market risk premium
• This ß is a multiplier which has to do with the
  relative risk premium of a security to the market
  risk premiumit is a relative Market (systematic)
  Risk

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SML

• RiRF RRP, then
• Security risk premium (Ri- RF)
• Market risk premium (Rm- RF)
• If security risk premiumß x market risk premium
• Then, (Ri- RF) ß x (Rm- RF)
• That is,
• Ri RF ß x (Rm - RF)
• This is also known as the SML (market
  equilibrium), a component of the CAPM
• As a result, any securitys return can calculated
  using ß, RRF, and Rm

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Graph of SML

• What if the observed returns are different from
  the theoretical returns?
• The Alpha-strategy consists of finding securities
  with abnormal excess return.

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Example 15 SML Questions

• What is the market relative risk (ß)?
• What does a ß of 2 mean?
• What does a ß of 1 mean?
• How do we get ß?
• What is the ß of a portfolio?

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Problems With SML

• 1. Beta coefficients are not stable for
  individual securities.
• Performance evaluation depends upon the choice
  of the market proxy.
• T-bills are not exactly risk-free
• Unpleasantries have been neglected (taxes and
  transaction cost)

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Example 16 Questions

• What is the difference between the CML and SML?
  Why are the measures of risk different?
• RP Rf (Rm Rf) /sm x sp ?CML
  (allocation)
• Ri Rf (Rm-Rf) x si/ sm x ?i,m ?SML
  (selection)
• Ri Rf (Rm-Rf) x ßi,m

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Example 17 what is the separation theorem?

• How is the concept of leverage included in the
  CML?

Wrfgt0
Wrflt0
Wrf0
Where, Wrf1-(sP/sM)
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Example 18 What is the alpha strategy?

• Is it possible to find an asset which is above
  the CML? Then how can we use the SML to select
  underpriced securities?
• According to the SML
• Ri-Rf 0 ß x (Rm-Rf)
• In a regression format (Ri-Rf) a ß x (Rm-Rf)
  e
• Then (alpha strategy)
• if a is not significantly different from 0,
  security is fairly priced
• if a is significantly greater 0, security is
  underpriced
• if a is significantly smaller than 0, security is
  overpriced

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Alpha Strategy
x A
x B
a
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Alpha-strategy

• SML (Ri Rf) alpha beta x (Rm-Rf) e
• Example EXTR

Alpha Beta R2
EXTR (t-stat) 0.019 (2.28) 1.47 (4.57) 0.25
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Example 19 A simple illustration

• Assume RFR 6
• RM 12

E(RA) 0.06 0.70 (0.12-0.06) 0.102
10.2 E(RB) 0.06 1.00 (0.12-0.06) 0.120
12.0 E(RC) 0.06 1.15 (0.12-0.06) 0.129
12.9 E(RD) 0.06 1.40 (0.12-0.06) 0.144
14.4 E(RE) 0.06 -0.30 (0.12-0.06) 0.042
4.2
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Comparison of Required Rate of Return to
Estimated Rate of Return
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Plot of Estimated Returnson SML Graph
.22 .20 .18 .16 .14 .12 Rm .10 .08 .06 .04 .02
C
SML
A
E
B
D
.20 .40 .60 .80
1.20 1.40 1.60 1.80
-.40 -.20
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Lets conclude and summarize now

• Develop an investment policy statement
• Identify investment needs, risk tolerance, and
  familiarity with capital markets
• Identify objectives and constraints
• Investment plans are enhanced by accurate
  formulation of a policy statement
• ALLOCATION determine the market/sector weights
• Asset allocation determines long-run returns and
  risk, which success depends on construction of
  the policy statement
• (1) EFFICIENT FRONTIER and (2) CML
• CML EFFICIENT FRONTIER when T-Bill is included
  in the efficient set
• SELECTION determine undervalued securities
• Actual (observed of predicted) Return Vs. SML
  (fair) return
• Alpha Analysis Is the SML significantly
  violated?
• Optimal allocation between selected securities
  with the efficient frontier

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Example 20 CASE

• You gather the following information about two
  stocks A and B, the SP500 and the treasury bill

State Prob. E(Ra) E(Rb) E(SP500) Rtbill
Bad 25 20 -20 0 2
Average 40 10 20 5 2
Good 35 -5 40 10 2
Covariance A B SP500 Tbill
A 0.009619
B -0.02133 0.0531
SP500 -0.0037374 0.00865 0.0014749
Tbill 0 0 0 0
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Example 16 Continued

• 1.What is the probability to break-even if you
  invest in A?
• Find Z(mean-X)/standard deviation? X0 then
  you need the expected return and the standard
  deviation of A
• E(R) 25 x 2040x1035x(-5)7.25
• s(A)(0.009619)1/29.8
• Z7.25/9.80.74
• P(0.74)77 chance

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Example 20 Continued

• 2. What is diversification? Illustrate using a
  portfolio consisting of A and B.
• Refer to book and slides for the first part. For
  the second part use a three-case scenario as in
  example 6, i.e.,

E(R) s COV(A,B)
A 7.25 9.8 -0.02133
B 17 23.04
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Example 20 Continued

• 3. In the previous question, what would the
  allocation to A and B if you chose the minimum
  risk portfolio?
• If WaW then Wb1-W and the variance of the
  portfolio is

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Example 20 Continued

• 4.Which stock would you consider as an addition
  to a portfolio made of the SP500? Which stock
  would you consider for stand-alone portfolio?
• Stock to consider as an addition to a portfolio
  made of the SP500?Get the alpha of each stock
• First get the theoretical (CAPM) return, then
  subtract it to the expected return.
• To get CAPM return
• RaRfBETA(A) x (Rm-Rf)
• RbRfBETA(B) x (Rm-Rf)
• Rf is the treasury bill return2
• Rm is the sp500 return5.5 (it is the weighted
  average return for sp500)
• sM(0.0014749)1/23.84
• BETA(A)COV(A,M)/VAR(M) -0.0037374/
  0.0014749-2.53
• BETA(B) COV(B,M)/VAR(M) 0.00865/ 0.00147495.85
• Then
• RaRfBETA(A) x (Rm-Rf)2-2.533.5-6.86
• RbRfBETA(B) x (Rm-Rf)25.853.522.48
• ALPHA(A)7.25-(-6.86)14.11?Undervalued
• ALPHA(B)17-22.48 -5.48?Overvalued
• Then you would A to a well-diversified portfolio
  like A

88
Example 20 Continued

• Stock to consider for stand-alone portfolio? get
  the Coefficient of Variation
• Calculate the Coefficient of Variation
• CV(A)9.8/7.251.35
• CV(B)23.04/171.35
• There are basically equivalent in terms of reward
  to risk in a stand-alone portfolio
• 5.What is the difference between the CML and SML?
• Look at slides and book

89
Example 20 Continued

• 6. How much (proportions) would you invest in A
  and B in order to get a portfolio as risky as the
  market?
• The market has a beta of 1 Solve a system of two
  equations
• Wa x BETA(A)Wb x BETA(B)1
• WaWb100
• Then, Wb1-BETA(A)/BETA(B)-BETA(A)
• BETA(A)COV(A,M)/VAR(M) -0.0037374/
  0.0014749-2.53
• BETA(B) COV(B,M)/VAR(M) 0.00865/ 0.00147495.85
• Wb42
• So, Wa58

90
Example 20 Continued

• 7.You have created your AB portfolio, then you
  decide to sell A and invest the proceed in
  T-bills. What the new portfolio Expected return,
  standard deviation and beta?
• Wb42 Wa58? sell A, buy TB? Wrf58
• BETA(new portfolio)Wb x BETA(B) Wrf x BETA(Rf)
• And of course BETA(Rf)0 sRf 0
• So,
• BETA(new portfolio).42 x 5.852.46
• E(new portfolio).42 x 17 .58 x 28.3
• s (new portfolio).42 x 23.049.68 (from the
  portfolio risk equation with 2 assets, it
  simplifies a lot as sRf 0)

91
Example 20 Continued

• 8. What is the separation Theorem?
• Answer in Book