©Prof. P.V. Viswanath, 1997

- Chapter 1: The Investment Environment
- Chapter 2: Markets and Instruments
- Chapter 3: How Securities are Traded
- Chapter 5: Interest Rates and Risk Premiums
- Chapter 6: Risk and Risk Aversion
- Chapter 7: Capital Allocation Between the Risky Asset and the Risk-Free Asset
- Chapter 8: Optimal Risky Portfolios
- Chapter 9: The Capital Asset Pricing Model
- Chapter 14: Bond Prices and Yields
- Chapter 15: The Term Structure of Interest Rates
- Chapter 16: Fixed-Income Portfolio Management
- Chapter 18: Equity Valuation Models
- Chapter 24: Portfolio Performance Evaluation
- Learning Objectives by Chapter

The distinction between real and financial assets; our course will deal mainly with financial assets.

Real assets are net income-generating assets for society, whereas financial assets define the allocation of income among investors or members of society. Real assets only appear on the assets side of the balance sheet, whereas financial assets can appear on both sides of the balance sheet. In fact, if a financial asset appears on the asset side of one entity's balance sheet, it will appear on the liability side of the balance sheet of another entity. Examples of real assets are houses, plant & equipment, land, consumer durables, human knowledge. Examples of financial assets are stocks, bonds, mortgages, options.

The household sector, on net, holds financial assets, while the business sector, on net, issues financial assets. The main role of the government sector is to regulate the financial environment, although it, too, can hold and issue financial assets.

The material wealth of an economy is __primarily__
determined by its real assets. Its financial assets are important
in facilitating exchange of those assets and the income flow from
those assets between people. Hence, the role of financial assets
is __secondary__, though hardly unimportant. Given this
distinction, it should be clear that , we should first look at
real factors in trying to explain economic phenomena, and then at
financial or nominal factors.

Problem 1, 2, 3, 4.

The financial environment responds to the needs of the different clienteles that comprise the economy.

- Financial Intermediation
- Mutual Funds, Banks, Investment companies, insurance companies

- Investment Banking companies aid in the design and issuance of securities
- Financial Innovation and Derivatives
- Securitization of liabilities: E.g. pass-through securities, like the GNMA
- Creation of derivatives to aid in risk sharing
- creation of new securities as a reponse to
taxation and regulation
- Eurodollar market responding to Regulation Q
- Zero-coupon securities responding to peculiarities in taxation of bond income
- Dual funds responding to the asymmetric taxation of dividends and capital gains

Problem 7.

Different kinds of markets also come into being in response to investor and issuer needs:

- Direct Search market
- Brokered Market
- Primary Market for securities
- Block Transactions

- Dealer Market
- Secondary Market
- Auction Market

New trends:

- Globalization/International Market Integration
- Securitization of new kinds of liabilities like credit card debt
- Credit Enhancement
- Financial Engineering: bundling and unbundling of financial assets.

Problem 8, 9, 10.

- Treasury Bills

Conventions regarding price quotations- bank discount yield
- Effective Annual Yield
- Bond Equivalent Yield

- Certificates of Deposit
- Commercial Paper
- Banker's Acceptances
- Eurodollars
- Repos and Reverse Repos
- Federal Funds
- Broker's Calls
- The LIBOR Market

Problems 2, 3, 4, 6.

- Treasury Notes and Bonds
- Bond Quoting Conventions: Yield to Maturity
- Webnotes on Treasury Securities

- Federal Agency Debt
- Municipal Bonds
- Corporate Bonds
- Mortgages and Mortgage-Backed Securities

- Common Stock
- Residual Claim
- Limited Liability
- Stock Market Listings

- Preferred Stock

- Dow Jones Index (price weighted average)
- S&P 500 Stock Index (market-value weighted average)
- Equally weighed indexes
- Indexes based on geometric averages

Problems 8, 9.

Problems 13, 14, 15, and 17.

- Primary Market
- Equities
- Initial Public Offerings (IPOs)
- Seasoned new issues

- Bonds
- Public Offering
- Private Placement

- Equities
- Secondary Markets
- Stock exchanges
- NYSE
- AMEX
- Others

- The Over-the-Counter Market
- Third Market: Trading of exchange-listed securities on the OTC market
- Fourth Market: Direct Trading between investors in exchange-listed securities without a broker.

- Stock exchanges

Problem 1

- Market Order

instructs the floor broker to promptly execute the order at the most favorable price. - Limit Order

A buy limit order stipulates that the floor broker executes the order within the limit set by the customer. If it is a sell limit order, the broker cannot sell for an amount less than that stipulated. If the price is touched, it is not guaranteed that the order is executed, since price moves may be rapid. - Stop Order

A buy stop order is placed above the current market price and becomes a market order if the pirce is touched. A sell stop order is placed below the current market price. - Open orders: good until cancelled

these orders will continue to be placed for execution until cancelled by the customer, or filled.

Problems 2, 3, 4.

- The role of specialists in market-making on the NYSE
- Block Sales
- The SuperDOT system
- Trading on the OTC market
- Execution of order
- Costs of trading
- Broker's Commission
- Bid-asked spread
- Costs of suboptimal order execution
- front running
- paying for order flow

Problems 6, 7.

- Webnotes on Margin Purchases
- Problems 11, 12.

- Webnotes on Short Selling
- Problems 13, 14.

Interest rates reflect the price that an investor is paid for the use of his

money over time. If *r* is the interest rate per period,
then a riskless investment of $1 today will yield $(1+*r*)
in one year. Consequently, the price that an investor will be
willing to pay today for $1 in one year is 1/(1+*r*).

It is easy to see that the interest rate will affect the price of assets, defined as cashflow generating machines. The other important element in the pricing of risky assets is the price of risk. We will first discuss interest rates (reflecting the price of riskless cashflows) and then the price of risk.

__Determinants of Interest Rates__:

Interest rates have two components, a reward for postponing
consumption (real rate of interest), and a compensation for
expected changes in the value of money (inflation) itself. We can
write: *r **;** R - i*,
where *r* is the real rate of interest, *R* is the
nominal rate of interest, and *i* is the inflation rate. If
prices are expected to increase by 10%, then a nominal rate of
interest of 15% implies a real rate of interest (rate of return
measured in consumption goods, rather than in dollars) of 15 - 10
or 5%.

The real interest rate is determined by

- the supply of funds from savers, primarily households
- the demand for funds from business to be used to finance physical investments in plant, equipment, and inventories
- the government's net supply and/or demand for funds
- the Fed's actions

As usual, the higher the reward for saving/cost of borrowing (real interest rate), the higher the supply of funds (upward sloping supply curve), and the lower the demand for funds (downward sloping demand curve). The intersection determines the equilibrium real interest rate. The Federal Reserve Bank can affect supply by an expansionary (increase supply of funds) or restrictive (decrease supply of funds) monetary policy.

The equilibrium nominal interest rate is equal to the equilibrium real interest rate plus the expected rate of inflation.

Problems 2, 3, 11.

Define holding period return.

We can now talk about the reward for bearing risk. Risk means uncertainty about future rates of return. This uncertainty is usually quantified as the variance of returns. Historically, classes of securities with higher return variances have yielded higher average returns as well.

Problems 4, 5, 15, 16.

However, the riskiness of a security has to be considered in the context of the portfolio in which the security is held. Sometimes movements in the value of a given security are offset by movements in the value of other securities. This reduces the uncertainty of a portfolio containing both those securities. Hence investors will be compensated only for certain kinds of risk (called non-diversifiable risk). We will see later how risk is properly defined and how we can define the relationship between risk and return.

Problem 17.

Another concept that is important in the pricing of assets is that of arbitrage. Arbitrage is the pricing of an asset at one price and simultaneously selling it (or its equivalent) at a higher price. Obviously, arbitrage possibilities cannot exist in a well-functioning market. This is another concept that is used in asset pricing. For example, the cash flows from stock options can be replicated by portfolios of stocks and bonds. Clearly, this implies that the option can be priced off the stocks and the bonds.

We start out looking at risk from an individual's point of view and the end up in Chapter 8 with a look at risk and return from a market point of view.

Problem 1.

We saw in chapter 4 that risk can be measured by variance of return. The reward for bearing this variance risk is a higher return on average. Depending on one's aversion to risk, some investors might demand a higher expected return and others, not so high an expected return for a given level of risk. If we assume that a higher expected return is a good and variance uncertainty is a bad, we can score the desirability of an investment portfolio using utility functions (5.1).

Problem 2.

The notion of indifference curves. The y-intercept of a given indifference curve can be thought of as the certainty equivalent of all the portfolios located on that indifference curve.

Problems 3, 7, 8, 9.

Asset risk versus portfolio risk. Example with two risky
investments: a consumer of sugar, and a producer of sugar.

Covariance measures the degree to which two assets move together.

Problems 13, 14 and 15.

In the last chapter, we learnt about risk and return. Ultimately, we will systematize our understanding of the relationship between risk and return. Before going on, however, we need to develop some portfolio mathematics. Fortunately, we can also learn about asset-allocation while we are about it.

We know that investing in stocks is can be risky. However, we can reduce the risk somewhat by investing in riskfree securities. How do we figure out the optimal amount to invest in risky stocks as opposed to the riskfree asset?

Portfolios of one risky asset and one riskfree asset

- Computation of the mean return and variance of returns for such a portfolio. (Equations 6.1 and 6.2)

- Problems 1, 2, 19, 20

- Problems 3, 4

- Problems 5, 6, 7

- Active strategies involve a lot of trading and expense
- free-rider benefit: with efficient markets, securities
are usually not grossly mispriced

(A discussion of efficient markets can be found in my Webnotes on the topic.)

- Problems 8, 9

- Classroom Project: Portfolio Analysis with two assets

Webnotes on Capital Allocation Between a Risky Asset and a Riskless Asset

- Formulas for Variance and Expected Return of Portfolios
- Use this to show that the Portfolio Variance can be thought of as a weighted average of the average variance and the average covariance between assets in the portfolio (Equation 7A3, page 227).
- Using the correlation, we can write the portfolio variance as equal to the average variance times a factor, which is a weighted average of unity and the average correlation coefficient. As the number of assets becomes large, the covariance/correlation term dominates. Consequently, in the limit, in a large, diversified portfolio, the portfolio variance is equal to the average correlation times the average variance. In what follows, we investigate how to diversify optimally.

Problems 15, 16 and 17

- Define Combination Line and Efficient Portfolios
- Define Reward-to-Variability Ratio as the Slope of the Combination Line
- Formula for Minimum Variance Portfolio (Equation 7.7)
- Formula for Optimal Portfolio (Fn. 7, p. 202) (Utility Based)

- Formula for Efficient Portfolio (Equation 7.8)
- Define Reward-to-Variability Ratio as the Slope of the Efficient Frontier/Opportunity Set (Figure 7.7)
- Formula for Optimal Portfolio (Equation 7.9) (Utility Based)

Problems 6, 7, 21.

- Figure 7.10 (p. 211)
- Once we determine the efficient frontier (opportunity set), the situation is similar graphically to the one for two risky assets and one risky asset.
- Note that the optimal risky portfolio is the same for everybody.

- Webnotes on Techniques for Constructing Efficient Portfolios
- Excel file demonstrating how to compute an optimal portfolio with > 2 assets

- Classroom Project: Portfolio Analysis with more than two assets.

Webnotes on Optimal Risky Portfolios

The CAPM gives us an *equilibrium* relationship between
risk and expected return. Two things should be noted regarding
this relationship:

- This may not describe the actual relationship between expected return and risk at any point.
- The posited relationship is unlikely to hold exactly for estimates of beta and expected return

An integrated presenation of the equilibrium relationship between risk and return starting with the concept of probability can be found in my Webnotes on Determination of the Discount Rate for Risky Assets.

- Many price-taking investors
- a single holding period
- all assets are traded, and investors can borrow and lend at the riskfree rate
- No taxes or other frictions
- Investors only care about mean and variance of returns
- all investors have the same information

- All investors hold assets in exactly the same proportion as in the market portfolio, i.e. the global portfolio of all assets in the economy.
- The market portfolio is mean-variance efficient, i.e the Capital Market Line, the line from the riskfree rate through the market portfolio is the best available Capital Allocation Line for all Investors
- The risk premium on the market portfolio will be proportional to the degree of risk aversion of the average investor in the market, and to the variance of the returns on the market portfolio.
- The risk premium on
*individual*assets will be proprtional to the risk premium on the market portfolio, and the beta coefficient of the security relative to the market portfolio.Problems 1, 2

- Why do all investors hold the market portfolio? Is this true in practice? If not, why not?
- Implications for Passive Investing/Mutual Funds
- What determines the market risk premium?
- Why is the risk definition for individual securities different from the risk definition for efficient portfolios, such as the market portfolio?
- The Security Market Line as a risk-reward relationship.

Webnotes on the Capital
Asset Pricing Model

Demonstration
of CAPM (in Excel)

Problems 3, 5, 6-12, 22, 23, 24.

- Classroom Project: Beta Computation

A brief discussion of the issues and concepts below can be found in my Webnotes on Bonds: Description and Introduction to Pricing. Note that these notes are in Rich Text Format (RTF). Can be read with Word for Windows and many other word-processing programs, such as WordPad.

What is a bond?

Types of bonds

- Treasury bonds
- Corporate Bonds
- Call Provisions on Corporate Bonds
- Convertible bonds
- Puttable Bonds
- Floating-Rate Bonds
- Preferred Stock
- Junk Bonds

Problem 22, 26.

- Bond Yields
- Yield to maturity and default risk
- Realized compound yield
- holding period return

Problems 2, 3, 5, 7, 9, 16, 19

An integrated description of bonds, their pricing, the term structure of interest rates, and bond portfolio management can be found in my Webnotes on Bond Pricing, Term Structure of Interest Rates, and Interest Rate Management. Note that this is in Word format. Click here for information on downloading.

- short interest rate
- yield curve using zero-coupon bonds
- yield curve using coupon bonds
- spot rate
- Holding period returns
- forward interest rate

Problems 5, 6, 13,

- Computer exercise
- Excel file on estimating forward rates

- liquidity premium
- theories of the term structure
- interpreting the term structure

Problems 2, 3, 17.

A detailed discussion of Fixed-Income Portfolio Management can be found in my Webnotes.

- Interest Rate Sensitivity
- Duration

Derivation of the duration formula - Rules for duration computation

Problems 1, 2, 6, 7

- Net Worth Immunization
- Target Date Immunization
- Immunization with Multiple Liabilities
- Rebalancing
- Cash Flow Matching and Dedication
- Interest Rate Swaps

Problems 11, 12, 13, 14

Problem 17, 18.

Much of the material for this chapter is taken from Aswath Damodaran's
book on Corporate
Finance, Chapter 23, titled *Basics of Valuation*. A
more detailed version of these notes can be found in My Webnotes on Equity Valuation. A simpler,
more introductory approach to Stock Valuation can be found in my Webnotes on Valuing Stocks.

There are two basic approaches to Valuation:

- Discounted Cashflow Valuation - the value of an asset is sought to be obtained directly by valuing the cashflows generated by that asset.
- Relative Valuation - the value of an asset is established relative to other assets.

However, one must recognize that all valuation is ultimately relative, and there are elements of relative valuation in discounted cashflow valuation as well, although this may sometimes be implicit.

The value of any asset is the present value of its expected cash flows.

The value of equity is the value of the equity stake in a business. In the context of a publicly traded firm, it is the value of the common stock in the firm.

The value of the firm is the total value of debt and equity in a business.

__Dividend Discount Model: __

The value of stock is the present value of dividends per share through infinity.

A certain pattern of dividends has to be assumed before this general model can be implemented to estimate the value of equity.

The most common assumption is that dividends will have a period of extraordinary growth followed by stable growth forever. This model needs four inputs:

- the length of the high-growth period
- dividends per share during the high-growth period.
- the terminal price at the end of the high-growth period.
- the rate of return demanded by investors or the discount rate.

Expected dividends during the high growth period can be estimated by first estimating expected earnings and then the dividend payout ratio; expected dividends are the product of the two. Expected earnings can be estimated by three appproaches:

- historical growth
- analyst projections
- fundamentals of the firm.

__FCFE Valuation Model: __

This model estimates the value of euqiyt as the present value of the expected free cashflows to equity over time.

FCFE = Net Income + Depreciation - Capital Expenditure - Change in Non-cash Working capital - Principal Repayments + New Debt issues.

As in the dividend discount model, there are four basic inputs to the model. A two-stage model similar to the dividend model is used here as well.

The FCFE Valuation method will provide identical estimates to the Dividend discount model when:

- dividends are equal to FCFE or
- the excess of FCFE over dividends is invested in zero NPV projects.

Often, the FCFE estimate is higher; the difference can provide valuable information about the firm's investment, financing and dividend policy.

__FCFF (Free cash flow to the firm) Valuation Model:__

The FCFF can be estimated as:

FCFF = Free cash flow to Equity + Interest expense (1 - tax rate) + Principal repayments - New debt issues + Preferred dividends.

FCFF = EBIT(1-tax rate) + Depreciation - Capital Expenditure - change in working capital

A two stage model similar to the FCFE model is used, except that the free cash flows are discounted at the firm's weighted average cost of capital. The growth rate in the FCFE model is usually greater than the growth rate in the FCFF model because of the existence of financial leverage.

The value of equity can be computed as the firm value less the value of debt less the value of preferred stock.

Discounted Cash-flow estimation may be difficult or impossible to use in the following circumstances:

- Firms in Trouble
- Cyclical Firms
- Firms with Unutilized Assets
- Firms with patent or product options
- Firms in the process of restructuring
- Firims involved in acquisitions
- Private Firms

The value of an asset is derived from the pricing of "comparable" assets, standardized using a common variable such as earnings, cash flows, book value, or revenues.

__Ways of using multiples__

- to use fundamentals
- to use comparables

Multiples can be misused because of the difficulty of finding comparables.

A more detailed discussion of these issues can be found in my Webnotes on Portfolio Evaluation.

- Time-weighted versus dollar-weighted returns
- Arithmetic Averages versus geometric averages

- Sharpe's Measure
- Treynor's Measure
- Jensen's Measure
- Appraisal Ratio

Chap | What you should know after completing
the chapter Warning! This is not an exhaustive listing |

1: | Differences between real and financial
assets the relationships between different market sectors Markets and securities evolve to meet the needs of the different sectors. |

2 | the different financial instruments
available to the investor the interpretation, composition and calculation of different market indexes the basics of options and futures contracts |

3 | How securities are traded on the primary
and secondary markets the mechanics, risk and calculations involved in margin and short trading. What are mutual funds? |

5 | The determinants of real and nominal
interest rates The effect of inflation on nominal interest rates Computation of expected return and standard deviation for various investment alternatives. The law of one price and the implications for arbitrage opportunities. |

6 | Risk and Risk aversion Risk, speculation and gambling Risk aversion and utility values Asset risk versus portfolio risk The statistical measure of portfolio risk |

7 | Risk reduction and the risk-free
asset portfolios of one risky and one risk-free asset risk tolerance and asset allocation Passive investment strategies using the capital market line |

8 | Diversification and portfolio risk
Creating Optimal Portfolios Using the Markowitz security selection algorithm The separation property of asset allocation |

9 | The theory of the Capital Asset Pricing
Model Construction and use of the security market line Extensions of the CAPM to allow for liquidity differences across stocks |

14 | Pricing, characteristics and risk
determinants of bonds Calculation of yields and prices of different kinds of bonds |

15 | The term structure of interest rates
under certainty and under uncertainty The three term structure hypotheses. |

16 | Duration and bond price
sensitivity Passive and Active Bond Portfolio strategies: their uses and their limitations. |

18 | Dividend Discount Model (DDM) Gordon Growth Model Combining P/E ratio forecasts and the DDM |

25 | The different measures of portfolio
evaluation Factors affecting portfolio performance: risk, timing, asset allocation, and security selection.Different ways of computing portfolio returns |

28 | Evaluation of the market timing ability
of portfolio managers Treynor-Black model of efficient security analysis Security analysis in multifactor security models. |