Principles of Finance

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Principles of Finance

• Bartek Kubicki
• City University, Trencin
• March 7th, 2009

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TODAYS SESSION

• Portfolio theory
• Capital Market Efficiency
• Cost of Capital

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PORTFOLIO THEORY

• the expected return for a portfolio of risky
  assets is the weighted average of the expected
  return of the individual assets in the portfolio
• portfolio risk (standard deviation) is NOT only a
  function of the standard deviation of returns of
  the individual assets in the portfolio. It is
  also a function of the correlations between the
  returns of the assets in the portfolio

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PORTFOLIO THEORY

• The general formula for the variance for a
  portfolio of n risky assets is as follows
• Therefore, for a 2 stock portfolio we have

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PORTFOLIO THEORY

• Calculate the return and standard deviation of a
  two-stock portfolio where
• The weights of the stocks in the portfolio are
  50 stock X, 50 stock Y. The correlations are
  -1, -0.5, 0, 0.5, 1
• Expected return 18

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PORTFOLIO THEORY

• Standard deviation
• WHEN ASSET RETURNS ARE NOT PERFECTLY POSITIVELY
  CORRELATED, DIVERSIFICATION CAN REDUCE THE
  PORTFOLIO RISK FOR A GIVEN LEVEL OF RETURN.

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PORTFOLIO THEORY

• Lets assume, the correlation between stock X and
  stock Y is 0.5. Manipulating with the weights we
  get the following results

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PORTFOLIO THEORY

• Combining weights and correlation manipulations

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PORTFOLIO THEORY

• And a scatter plot
• THE EFFICIENT FRONTIER represents the set of
  portfolios that will give you the highest return
  at each level of risk

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PORTFOLIO THEORY

• Investors choice of the most preferred portfolio
  will depend on his risk-aversion

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PORTFOLIO THEORY

• Unsystematic risk the risk that disappears in
  the portfolio construction process, unique risk
• Systematic risk non-diversifiable or market risk

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PORTFOLIO THEORY
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PORTFOLIO THEORY

• Adding risk-free asset
• changes the Markowitz efficient frontier from a
  curve into a straight line called capital market
  line (CML)
• market portfolio is at the point where the
  risk-return trade-off line is just tangent to the
  efficient frontier
• all investors combine the tangent (market)
  portfolio with the risk free-asset in accordance
  with their risk aversion
• since all investors will want to hold the same
  risky portfolio, i.e. the market portfolio, it
  has to consist of all the risky assets

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PORTFOLIO THEORY

• ASSUMPTIONS
• Markowitz investors (mean-variance framework)
• Unlimited risk-free lending and borrowing
• Homogeneous expectations
• One-period horizon
• Divisible assets
• Frinctionless markets
• No inflation and constant interest
• Equilibrium

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PORTFOLIO THEORY
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PORTFOLIO THEORY

• IMPLICATIONS
• Equilibrium security returns depend on a stocks
  or a portfolio systematic risk, not its total
  risk as measured by standard deviation
• Diversification is free then why to compensate
  for risk that an investor can eliminate himself?
• The proper risk measure for systematic risk is
  beta

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PORTFOLIO THEORY
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PORTFOLIO THEORY

• The SML intersects the y-axis at the point of the
  risk-free rate of return
• The trade off between risk and return is shown by
  movement on the SML
• The slope of the SML reflects the market risk
  premium (investors attitude towards risk)
• If the market risk premium increases, the SML
  will rotate counterclockwise
• If the market premium decreases, the SML will
  rotate clockwise

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PORTFOLIO THEORY

• If the inflation expectations increase
  (decrease), the SML will shift upward (downward)
  in a parallel fashion
• If the economic growth increases (decreases), the
  SML will shift upward (downward) in a parallel
  fasion
• If the capital market tighten (loosen), the SML
  will shift upward (downward) in a parallel
  fashion

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PORTFOLIO THEORY

• Suppose Rf 7, covariance (j, M) 250, s2M
  225, RM 15. What is security j required
  return?
• 15.88
• What shall we do with the stock if we actually
  expect the return to be 20? Where would it be on
  the chart?
• What problems to you see with CAPM in reality?

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PORTFOLIO THEORY

• An analyst is forecasts are in the table. Assume
  a risk-free rate of 7 and a market return of
  15. Compute the expected and required return on
  each stock, determine whether each stock is
  undervalued, overvalued, or properly valued, and
  outline an appropriate trading strategy.
• A overvalued, B undervalued, C properly
  valued

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PORTFOLIO THEORY

• TESTING CAPM
• Beta changes significantly over time (the longer
  the period the better)
• Portfolio betas tend to be stable than individual
  betas
• Benchmark error problem (not diversified enough)

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CAPITAL MARKET EFFICIENCY

• EFFICIENT CAPITAL MARKET is a market in which
  the current price of a security fully reflects
  all the information currently available about the
  security, including risk
• INFORMATIONALLY EFFCIENT MARKET is one in which
  security prices adjust rapidly and completely to
  new information

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CAPITAL MARKET EFFICIENCY

• ASSUMPTIONS
• a large number of profit maximizing participants
• new information appears randomly
• investors adjust the price rapidly
• the adjustment might not be correct, just
  unbiased
• expected return implicitly include risk in the
  price

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CAPITAL MARKET EFFICIENCY

• WEAK-FORM EFFICIENT MARKET current stock prices
  fully reflect all currently available security
  market information
• SEMISTRONG-FORM EFFICIENT MARKET current stock
  prices fully reflect all publicly available
  information (market and non market)
• STRONG-FORM EFFICIENT MARKET stock prices fully
  reflect all information from public and private
  sources

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CAPITAL MARKET EFFICIENCY

• PERFECT CAPITAL MARKET
• No entry barriers
• Perfect competition
• Assets are infinitely divisible
• No transaction costs
• All information is fully available
• No tax asymmetries
• No government and other restrictions on trading

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CAPITAL MARKET EFFICIENCY

• WEAK-FORM autocorrelation tests, trading rule
  tests trading rules cannot generate positive
  abnormal returns after incorporating trading
  costs
• SEMISTRONG-FORM event studies, time-series test
  mixed results, market are not always semistrong
  efficient
• STRONG-FORM insider trading, exchange
  specialist, security analysts, money managers
  insiders and specialist do make abnormal returns

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CAPITAL MARKET EFFICIENCY

• SOME OF THE REPORTED ANOMALIES
• earnings surprises
• calendar studies (January effect)
• P/E ratio
• size effect
• neglected firm effect
• P/BV

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CAPITAL MARKET EFFICIENCY

• IMPLICATIONS
• Technical analysis
• Fundamental analysis
• Portfolio managers
• Financing decisions
• MA, LBO, PE (value additivity)

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COST OF CAPITAL

• COST OF CAPITAL opportunity cost, required rate
  of return it is the rate at which investors
  would provide financing for the capital budgeting
  under consideration today

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COST OF CAPITAL

• COST OF DEBT calculated on an after-tax basis.
  It is the interest rate at which firms can issue
  new debt net of tax savings
• Kd interest (1-t)
• Company X is planning to issue new debt at an
  interest rate of 8. X has a marginal tax rate of
  40. What is the cost of debt?
• 4.8

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COST OF CAPITAL

• COST OF PREFERRED STOCK
• kS DS / Pnet
• Pnet net issuing price after deducting
  flotation costs
• Company X has preferred stock that pays 8
  dividend per share and sells for 100 per share.
  If X were to issue new shares of preferred, it
  would incur a flotation cost of 5. What is Xs
  cost of preferred stock?
• 8.4

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COST OF CAPITAL

• COST OF COMMON STOCK
• 1. CAPM kCS RF ß(RM RF)
• 2. Bond yield risk premium
• 3. Dividend yield plus growth rate kCS (D1 /
  P0) g
• Company Xs stock sells for 21, last dividend
  was 1, dividend growth rate is 8. What is the
  cost of newly issued equity if the flotation cost
  is 10?
• 13.71

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COST OF CAPITAL

• WEIGHTED AVERAGE COST OF CAPITAL (WACC)
• Is the weighted average (weights are the
  market values of capital components) of the
  required return on equity and debt. It is the
  average cost of all funds. Weights are based on
  the firms target (optimal) capital structure.
• Capital structure that maximizes the value
  of the company is the capital structure that
  minimizes WACC.

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COST OF CAPITAL

• The company has a target capital structure of 40
  debt and 60 equity. Bonds with face value of
  1,000 pay 10 coupon (semiannual), mature in 20
  years, and sell for 849.54. The stock beta is
  1.2, risk free rate is 10, and a market risk
  premium is 5. The company is constant-growth
  firm that just paid a dividend of 2, sells for
  27 per share and has a growth rate of 8. The
  marginal tax rate equals 40. Calculate cost of
  debt, cost of equity (CAPM and dividend discount
  approach), WACC, if flotation cost is 10 what is
  the cost of new equity, and new WACC?
• 7.2, 16, 16, 12.48, 16.9, 13.02