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Corporate Finance

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Corporate Finance ­FIN 622
VU
Lesson 16
PORTFOLIO & DIVERSIFICATION
The following topics will be discussed in this lecture.
Portfolio and Diversification
Portfolio and Variance
Risk ­ Systematic & Unsystematic
Beta ­ Measure of systematic risk
Aggressive & defensive stocks
Modern Portfolio Theory (MPT) proposes how rational investors will use diversification to optimize their
portfolios, and how an asset should be priced given its risk relative to the market as a whole. The basic
concepts of the theory are Mark with diversification, the efficient frontier, capital asset pricing model and
beta coefficient, the Capital Market Line and the Securities Market Line.
MPT models the return of an asset as a random variable and a portfolio as a weighted combination of
assets; the return of a portfolio is thus also a random variable and consequently has an expected value and a
variance. Risk in this model is identified with the standard deviation of portfolio return. Rationality is
modeled by supposing that an investor choosing between several portfolios with identical expected returns
will prefer that portfolio which minimizes risk.
Risk and Reward
The model assumes that investors are risk averse. This means that given two assets that offer the same
return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if
compensated by higher expected returns. Conversely, an investor who wants higher returns must accept
more risk. The exact trade-off will differ by investor. The implication is that a rational investor will not
invest in a portfolio if a second portfolio exists with a more favorable risk-return profile - i.e. if for that level
of risk an alternative portfolio exists which has better expected returns.
Mean and Variance
It is further assumed that investor's risk / reward preference can be described via a quadratic utility
function. The effect of this assumption is that only the expected return and the volatility (i.e. mean return
and standard deviation) matter to the investor. The investor is indifferent to other characteristics of the
distribution of returns, such as its skew. Note that the theory uses a historical parameter, volatility, as a
proxy for risk while return is an expectation on the future.
Under the model:
·  Portfolio return is the component-weighted return (the mean) of the constituent assets. Return
changes linearly with component weightings, wi.
·  Portfolio volatility is a function of the correlation of the component assets. The change in volatility
is non-linear as the weighting of the component assets changes.
Diversification
An investor can reduce portfolio risk simply by holding instruments which are not perfectly correlated. In
other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of
assets. Diversification will allow for the same portfolio return with reduced risk. For diversification to work
the component assets must not be perfectly correlated, i.e. correlation coefficient not equal to 1.
Capital Allocation Line
The Capital Allocation Line (CAL) is the line that connects all portfolios that can be formed using a risky
asset and a risk-less asset. It can be proven that it is a straight line and that it has the following equation.
In this formula P is the risky portfolio, F is the risk-less portfolio and C is a combination of portfolios P
and F.
The Efficient Frontier
Every possible asset combination can be plotted in risk-return space, and the collection of all such possible
portfolios defines a region in this space. The line along the upper edge of this region is known as the
efficient frontier (sometimes "the Mark witz"). Combinations along this line represent portfolios for which
there is lowest risk for a given level of return. Conversely, for a given amount of risk, the portfolio lying on
the efficient frontier represents the combination offering the best possible return. Mathematically the
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Corporate Finance ­FIN 622
VU
Efficient Frontier is the intersection of the Set of Portfolios with Minimum Variance and the Set of
Portfolios with Maximum Return.
The efficient frontier will be concave ­ this is because the risk-return characteristics of a portfolio change in
a non-linear fashion as its component weightings are changed. (As described above, portfolio risk is a
function of the correlation of the component assets, and thus changes in a non-linear fashion as the
weighting of component assets changes.)
The region above the frontier is unachievable by holding risky assets alone. No portfolios can be
constructed corresponding to the points in this region. Points below the frontier are suboptimal. A rational
investor will hold a portfolio only on the frontier.
The Risk-Free Asset
The risk-free asset is the (hypothetical) asset which pays a risk-free rate - it is usually provied by an
investment in short-dated Government bonds. The risk-free asset has zero variance in returns (hence is
risk-free); it is also uncorrelated with any other asset (by definition: since its variance is zero). As a result,
when it is combined with any other asset, or portfolio of assets, the change in return and also in risk is
linear.
Because both risk and return change linearly as the risk-free asset is introduced into a portfolio, this
combination will plot a straight line in risk return space. The line starts at 100% in cash and weight of the
risky portfolio = 0 (i.e. intercepting the return axis at the risk-free rate) and goes through the portfolio in
question where cash holding = 0 and portfolio weight = 1.
Portfolio Leverage
An investor can add leverage to the portfolio by holding the risk-free asset. The addition of the risk-free
asset allows for a position in the region above the efficient frontier. Thus, by combining a risk-free asset
with risky assets, it is possible to construct portfolios whose risk-return profiles are superior to those on the
efficient frontier.
·  An investor holding a portfolio of risky assets, with a holding in cash, has a positive risk-free
weighting (a de-leveraged portfolio). The return and standard deviation will be lower than the
portfolio alone, but since the efficient frontier is convex, this combination will sit above the
efficient frontier ­ i.e. offering a higher return for the same risk as the point below it on the
frontier.
·  The investor who borrows money to fund his/her purchase of the risky assets has a negative risk-
free weighting -i.e. a leveraged portfolio. Here the return is geared to the risky portfolio. This
combination will again offer a return superior to those on the frontier.
The Market Portfolio
The efficient frontier is a collection of portfolios, each one optimal for a given amount of risk. A quantity
known as the Sharp ratio represents a measure of the amount of additional return (above the risk-free rate)
a portfolio provides compared to the risk it carries. The portfolio on the efficient frontier with the highest
Sharpe Ratio is known as the market portfolio, or sometimes the super-efficient portfolio. This portfolio
has the property that any combination of it and the risk-free asset will produce a return that is above the
efficient frontier - offering a larger return for a given amount of risk than a portfolio of risky assets on the
frontier would.
Capital Market Line
When the market portfolio is combined with the risk-free asset, the result is the Capital Market Line. All
points along the CML have superior risk-return profiles to any portfolio on the efficient frontier. (A
position with zero cash weighting is on the efficient frontier - the market portfolio.)
The CML is illustrated above, with return μp on the y axis, and risk σp on the x axis.
One can prove that the CML is the optimal CAL and that its equation is:
Asset Pricing
A rational investor would not invest in an asset which does not improve the risk-return characteristics of his
existing portfolio. Since a rational investor would hold the market portfolio, the asset in question will be
added to the market portfolio. MPT derives the required return for a correctly priced asset in this context.
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Corporate Finance ­FIN 622
VU
Systematic Risk and Specific Risk
Specific risk is the risk associated with individual assets - within a portfolio these risks can be reduced
through diversification (specific risks "cancel out"). Systematic risk, or market risk, refers to the risk
common to all securities - except for selling short as noted below, systematic risk cannot be diversified away
(within one market). Within the market portfolio, asset specific risk will be diversified away to the extent
possible. Systematic risk is therefore equated with the risk (standard deviation) of the market portfolio.
Since a security will be purchased only if it improves the risk / return characteristics of the market portfolio,
the risk of a security will be the risk it adds to the market portfolio. In this context, the volatility of the asset,
and its correlation with the market portfolio, is historically observed and is therefore a given (there are
several approaches to asset pricing that attempt to price assets by modeling the stochastic properties of the
moments of assets' returns - these are broadly referred to as conditional asset pricing models). The
(maximum) price paid for any particular asset (and hence the return it will generate) should also be
determined based on its relationship with the market portfolio.
Systematic risks within one market can be managed through a strategy of using both long and short
positions within one portfolio, creating a "market neutral" portfolio.
Security Characteristic Line
The Security Characteristic Line (SCL) represents the relationship between the market return (rM) and
the return of a given asset i (ri) at a given time t. In general, it is reasonable to assume that the SCL is a
straight line and can be illustrated as a statistical equation:
where αi is called the asset's alpha coefficient and βi the asset's beta coefficient.
Capital asset pricing model
The asset return depends on the amount paid for the asset today. The price paid must ensure that the
market portfolio's risk / return characteristics improve when the asset is added to it. The CAPM is a model
which derives the theoretical required return (i.e. discount rate) for an asset in a market, given the risk-free
rate available to investors and the risk of the market as a whole.
The CAPM is usually expressed:
·
β, Beta, is the measure of asset sensitivity to a movement in the overall market; Beta is usually
found via regression on historical data. Betas exceeding one signify more than average "risk ness";
betas below one indicate lower than average.
·
is the market premium, the historically observed excess return of the market
over the risk-free rate'
Once the expected return, E(ri), is calculated using CAPM, the future cash flows of the asset can be
discounted to their present value using this rate to establish the correct price for the asset. (Here again, the
theory accepts in its assumptions that a parameter based on past data can be combined with a future
expectation.)
A more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will
have lower betas and be discounted at a lower rate. In theory, an asset is correctly priced when its observed
price is the same as its value calculated using the CAPM derived discount rate. If the observed price is
higher than the valuation, then the asset is overvalued; it is undervalued for a too low price.
Securities Market Line
The relationship between Beta & required return is plotted on the securities market line (SML) which shows
expected return as a function of β. The intercept is the risk-free rate available for the market, while the slope
is
. The Securities market line can be regarded as representing a single-factor model of
the asset price, where Beta is exposure to changes in value of the Market. The equation of the SML is thus:
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Corporate Finance ­FIN 622
VU
Comparison with Arbitrage Pricing Theory
The SML and CAPM are often contrasted with the Arbitrage pricing theory (APT), which holds that the
expected return of a financial asset can be modeled as a linear function of various macro-economic factors,
where sensitivity to changes in each factor is represented by a factor specific bets coefficient.
The APT is less restrictive in its assumptions: it allows for an explanatory (as opposed to statistical) model
of asset returns, and assumes that each investor will hold a unique portfolio with its own particular array of
betas, as opposed to the identical "market portfolio". Unlike the CAPM, the APT, however, does not itself
reveal the identity of its priced factors - the number and nature of these factors is likely to change over time
and between economies.
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Table of Contents:
  1. INTRODUCTION TO SUBJECT
  2. COMPARISON OF FINANCIAL STATEMENTS
  3. TIME VALUE OF MONEY
  4. Discounted Cash Flow, Effective Annual Interest Bond Valuation - introduction
  5. Features of Bond, Coupon Interest, Face value, Coupon rate, Duration or maturity date
  6. TERM STRUCTURE OF INTEREST RATES
  7. COMMON STOCK VALUATION
  8. Capital Budgeting Definition and Process
  9. METHODS OF PROJECT EVALUATIONS, Net present value, Weighted Average Cost of Capital
  10. METHODS OF PROJECT EVALUATIONS 2
  11. METHODS OF PROJECT EVALUATIONS 3
  12. ADVANCE EVALUATION METHODS: Sensitivity analysis, Profitability analysis, Break even accounting, Break even - economic
  13. Economic Break Even, Operating Leverage, Capital Rationing, Hard & Soft Rationing, Single & Multi Period Rationing
  14. Single period, Multi-period capital rationing, Linear programming
  15. Risk and Uncertainty, Measuring risk, Variability of return–Historical Return, Variance of return, Standard Deviation
  16. Portfolio and Diversification, Portfolio and Variance, Risk–Systematic & Unsystematic, Beta – Measure of systematic risk, Aggressive & defensive stocks
  17. Security Market Line, Capital Asset Pricing Model – CAPM Calculating Over, Under valued stocks
  18. Cost of Capital & Capital Structure, Components of Capital, Cost of Equity, Estimating g or growth rate, Dividend growth model, Cost of Debt, Bonds, Cost of Preferred Stocks
  19. Venture Capital, Cost of Debt & Bond, Weighted average cost of debt, Tax and cost of debt, Cost of Loans & Leases, Overall cost of capital – WACC, WACC & Capital Budgeting
  20. When to use WACC, Pure Play, Capital Structure and Financial Leverage
  21. Home made leverage, Modigliani & Miller Model, How WACC remains constant, Business & Financial Risk, M & M model with taxes
  22. Problems associated with high gearing, Bankruptcy costs, Optimal capital structure, Dividend policy
  23. Dividend and value of firm, Dividend relevance, Residual dividend policy, Financial planning process and control
  24. Budgeting process, Purpose, functions of budgets, Cash budgets–Preparation & interpretation
  25. Cash flow statement Direct method Indirect method, Working capital management, Cash and operating cycle
  26. Working capital management, Risk, Profitability and Liquidity - Working capital policies, Conservative, Aggressive, Moderate
  27. Classification of working capital, Current Assets Financing – Hedging approach, Short term Vs long term financing
  28. Overtrading – Indications & remedies, Cash management, Motives for Cash holding, Cash flow problems and remedies, Investing surplus cash
  29. Miller-Orr Model of cash management, Inventory management, Inventory costs, Economic order quantity, Reorder level, Discounts and EOQ
  30. Inventory cost – Stock out cost, Economic Order Point, Just in time (JIT), Debtors Management, Credit Control Policy
  31. Cash discounts, Cost of discount, Shortening average collection period, Credit instrument, Analyzing credit policy, Revenue effect, Cost effect, Cost of debt o Probability of default
  32. Effects of discounts–Not effecting volume, Extension of credit, Factoring, Management of creditors, Mergers & Acquisitions
  33. Synergies, Types of mergers, Why mergers fail, Merger process, Acquisition consideration
  34. Acquisition Consideration, Valuation of shares
  35. Assets Based Share Valuations, Hybrid Valuation methods, Procedure for public, private takeover
  36. Corporate Restructuring, Divestment, Purpose of divestment, Buyouts, Types of buyouts, Financial distress
  37. Sources of financial distress, Effects of financial distress, Reorganization
  38. Currency Risks, Transaction exposure, Translation exposure, Economic exposure
  39. Future payment situation – hedging, Currency futures – features, CF – future payment in FCY
  40. CF–future receipt in FCY, Forward contract vs. currency futures, Interest rate risk, Hedging against interest rate, Forward rate agreements, Decision rule
  41. Interest rate future, Prices in futures, Hedging–short term interest rate (STIR), Scenario–Borrowing in ST and risk of rising interest, Scenario–deposit and risk of lowering interest rates on deposits, Options and Swaps, Features of opti
  42. FOREIGN EXCHANGE MARKET’S OPTIONS
  43. Calculating financial benefit–Interest rate Option, Interest rate caps and floor, Swaps, Interest rate swaps, Currency swaps
  44. Exchange rate determination, Purchasing power parity theory, PPP model, International fisher effect, Exchange rate system, Fixed, Floating
  45. FOREIGN INVESTMENT: Motives, International operations, Export, Branch, Subsidiary, Joint venture, Licensing agreements, Political risk