University of MinnesotaMasters in Financial Mathematics OrientationAugust 27, 2008

Gary Hatfield

Modern Finance

Capital Structures and Risk Management

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Agenda

• What is Capital?• Typed of Capital and Capital Structure• Capital Asset Pricing Model (CAPM)• Modigliani – Miller (M&M)

– Without Corporate Income Taxes– With Taxes

• Why is M&M not practiced?• Why do risk management?

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What is Capital?

• Dictionary:  accumulated goods devoted to the production of other goods

• Example:– You want to start a business that makes and sells

ice cream to retail customers– You need money to purchase ice cream making

equipment, freezers, milk sugar, not to mention a store, is capital

– But you do not have enough money

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What is Capital?

• For the small business owner, capital can be raised via– Own savings– Business partner (investor)– Bank loan

• For large endeavors however, this means are rarely adequate

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Types of Capital

• How to raise a large amount of capital?• Rather than finding a small number of very

wealthy investors, find a large number of investors (who may or may not be individually wealthy)

• Stocks: Each share represents partial ownership in the firm

• Bonds: Basically, “I.O.U’s” issued by the firm and can traded by the initial investors

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Types of Capital

• Keys to success of stocks of bonds– Limited Liability of investors– Transparent and publically available information

on issuing firms– Liquid markets that allow stocks and bonds to be

traded

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Capital Structure

• Capital Structure refers to – How the firm has raised capital for its ventures– How the profits of the firm are divided among its

investors

• Generally speaking, this can be thought of in terms of how much is raised via stocks versus via bonds

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Capital Structure

• Stocks and bonds:– Bond holders get first rights up to amount of IOU– Stock holder are entitled to all profits beyond the

bond IOU’s

• Within each class (stocks and bonds), there can be further delineation of priority

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Capital Structure (Priority)

• Stocks 1. (Higher) Preferred stock

• Preferred stock pays a regular dividend as long there are fund available to pay it

• Preferred stock holders have no voting rights (i.e. no say in how the company is run)

• Preferred stock holders get nothing extra when profits are high

2. (lower) Common stock• Shareholders have control of the firm• Shareholders entitled to all excess profits

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Capital Structure (Priority)

• Bonds1. Senior – secured (certain assets pledged as

collateral)

2. Senior – unsecured

3. Subordinated

• Convertible bonds – “hybrid capital”

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Capital Asset Pricing Model (CAPM)

• Basic assumptions– Investors are risk averse and rational– Hence, for a given level of risk, investors prefer

investments with the highest expected return– Equivalently, for a given level of expected return,

investors prefer investments with the lowest amount of risk

– Standard deviation of returns is a good measure of risk

– All investors have the same view of risks and returns for all securities

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CAPM

• For each level of risk, the portfolio of risky assets with the highest expected return is called “efficient”

• The set of efficient portfolios for many levels of risk is called the “efficient frontier” of risky assets

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%Efficient Frontier

Risk

Ret

urn

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CAPM

• Suppose the risk-free investment yielding 4% is available, then the efficient frontier of all investments is combination of the risk free asset and an efficient risky portfolio

• This is also called the Capital Market Line

0.00% 2.00% 4.00% 6.00% 8.00% 10.00%12.00%14.00%16.00%18.00%0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%Efficient Frontier

Risk

Ret

urn

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The Market Portfolio

• The efficient risky portfolio whose tangent line intercepts with the risk free asset is therefore held in every efficient portfolio that includes the risk free asset as a choice

• Under the assumption of homogenous investors, this portfolio is the only risky asset portfolio that investors will hold (along with risk free bonds)

• This portfolio is called the Market Portfolio

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The Market Portfolio and beta

• The expected return on any given asset therefore depends on its correlation with the market portfolio

• Mathematically, this means that the expected return on a security can be written:

where riskfreemarketassetriskfreeasset RRRR

)(

),(

assetVariance

marketassetCovasset

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The Market Portfolio and beta

• Since beta depends only on the correlation with the market portfolio, it follows that variance in the returns that are uncorrelated with the market makes no difference in terms of the expected return of the security (equivalently, its price)

• In other words, the risk of a firm specific to that firm, called idiosyncratic risk, does not matter to investors

• The basic argument is that idiosyncratic risks can be diversified away

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CAPM

• Since firm specific risks earn no risk premium, it follows that risk management is of little value– Reducing beta accomplishes nothing, since

those risks cannot be reduced without paying risk premium equal to the amount of value added (i.e. you can only reduce beta risk by shorting the market)

– Reducing idiosyncratic risk is only an expense because idiosyncratic risks are not priced

• More on why these conclusions are likely not true later

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Modigliani and Miller (M&M)

• Back to capital structure• An important question for firms seeking to raise

capital is to find the right combination of stock versus bond

• Goal is to find the combination that maximizes the value the shareholder’s claims (since they are the owners)

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M&M

• Modigliani and Milled assumed– No corporate income taxes– No bankruptcy costs

=> Capital Structure is irrelevant!

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M&M (add taxes)

• In the U.S., firms pay 35% corporate income tax• M&M showed: in the presence of corporate

income taxes (everything else being the same), corporations should raise as much capital via bonds as possible (simple reason: interest paid on bonds is tax deductable but dividends are not)

• But clearly this is not the observed practice

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Why do companies not issue as much bonds as possible?

• Bankruptcy costs – higher debt levels increase the probability of default

• This explains part of the answer, but is of questionable value because the stock holders are not responsible for bankruptcy costs

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Risk Management and Capital Structure

• One the one hand, naïve financial models suggest;– Risk management adds no value– Firms should lever as much as possible (issue mostly

bonds and little equity)• On the other hand,

– Most companies expend a lot of money on risk management

– Most companies do not lever to the hilt(Fannie and Freddie excepted)

• Why?

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Value of the firm

• Firm Value = Value of Assets – Value of Debt + put option + franchise value

• Value of Assets – Value of Debt = liquidation value

• Put option refers to shareholders right to walk away without further liability

• Franchise value refers to present value of all future profits

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Value of the Firm

• Hypothesis:– Failure to manage risk and too much leverage

increase the likelihood of financial ruin– Financial ruin destroys franchise value

• However, if franchise value is easily created by deploying financial capital, then the argument does not work – Investors would more happily fund a start up than

an under water existing firm

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Value of the Firm

• But if franchise value is not easily created simply by deploying financial assets, then there is a good reason to avoid ruin

• Consider:– Reputation– Brand– Distribution and business relationships– Human Capital

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Summary

• Capital is the money needed to create goods• The composition and form of a firm’s capital is

its capital structure• CAPM suggests no reason to manage risk• M&M suggests levering to the max• Observed practice suggests otherwise• Hypothesis: Franchise Value is more easily

destroyed than created