Finance 2

Prof. Lars-Alexander Kuehn

Introduction

Present Value

Rate of Return

Options

Call option gives its buyer the right, but not the obligation, to buy one Tesla share at the strike price on the expiration day.

Coorperate Bonds

Enterprise Value

Enterprise Value = Debt + Equity

WACC

Weighted average cost of capital (WACC): Account for the tax shield by adjusting downward the discount rate used to value the future FCFs.

The weighted average cost of capital is given by:

Topic 1: Mean-Variance Investing

Definitions of Returns

Index Fund

An index fund is a mutual fund or exchange-traded fund (ETF) designed to track a financial index such as the S&P 500.

The S&P 500 is a stock market index that measures the stock performance of the 500 largest companies (measured by market capitalization, i.e., the value of equity) listed on stock exchanges in the United States.

• Mutual funds trade at the end of the day at net asset value (NAV).
• ETF trade continuously during the day at market prices, which might deviate from NAV.
• Mutual fund might generate capital gains when shares are sold, which are then distributed to shareholders before year-end.
• ETFs are more tax ecient than mutual funds because of the way they are created and redeemed.

How do you earn the cumulative total return?

• By reinvesting dividends.
• Index funds pay out dividends, which they collect from rms in the index. They do not reinvest dividends automatically for you.
• Your broker will reinvest dividends for you by buying more shares of the index fund.
• Dividends are taxed at either the ordinary income tax rate or the preferred long-term capital gains tax rate.

Average Performance

Simple and geometric averages can be computed for price and total return.

Excel commands: AVERAGE(...) and GEOMEAN(...)

Annual Return

\[r_a = (1 + r_1)(1 + r_2)...(1 + r_12) - 1\]

Risk

The standard deviation is often called volatility in nancial markets.

Exel command: STDEV.S(...)

Stock Splits

Dividends

Asset Classes

SPY; SHY; IEF; LQD

Crypto Asset

Portfolio Choice

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990

• Harry Markowitz for having developed the theory of portfolio choice.
• William Sharpe for his contributions to the theory of price formation for financial assets, the so-called, Capital Asset Pricing Model (CAPM).
• Merton Miller for his fundamental contributions to the theory of corporate finance.

Asset Allocation

Asset allocation is the portfolio choice among broad investment classes.

1. Two risky assets
2. Many risky assets
3. Many risky assets and a risk-free asset

Correlation between Risky Assets

A covariance is a measure of the joint variability of two random variables.

Excel commands: COVARIANCE.S(...) and CORREL(...)

Portfolio Frontier

• The portfolio frontier depicts the feasible portfolio choices for investors holding stocks and bonds.
• There exists a minimum variance portfolio (MVP).
• Portfolios below the minimum variance portfolio are inefficient.
• The portfolio frontier above the minimum variance portfolio is called efficient frontier.

(1)Two Risky Assets

• weight w in stock 1 with return r1
• weight (1-w) in stock 2 with return r2

(2)Many Risky Assets

(3)Many Risky Assets and a Risk-Free Asset

• v in the risky portfolio rp
• 1-v in risk-free bonds with return rf

Capital Allocation Line

• The CAL shows the risk-return combinations available by changing the proportion invested in a risk-free asset and a risky asset.
• The slope of the CAL is the so-called Sharpe ratio.

Optimal Capital Allocation Line

• The optimal capital allocation line combines the risk-free asset with the tangency portfolio of risky assets.
• The objective is to maximize the slope of the CAL = Sharpe ratio
• Two fund separation property: Every investor will invest in the same tangency portfolio of risky assets and the risk-free asset.

Preferences

Which risk-return combination along the CAL do you want? -> Your preferences for risk

Diversification vs. Concerntration

Do Stocks Outform Treasury Bills? No

• The mejority of common stocks since 1926 have lifetime cumulative returns less than one-month Treasuries.
• The best-performing 4% of listed companies explain the net gain for the entire U.S. stock market since 1926.
• Positive Skeness in the distribution of individual stock returns and the effects of compounding.
• Poorly-diversified active strategies most often underperform market averages.

Diversification cannot eliminate covariance risk.

The total risk of a portfolio:

1. Market (systematic) risk - Risk common to the whole economy / Cannot be diversified away
2. Firm-specific (idiosyncratic) risk - Risks which are specific to a company / Can be diversified away

Topic 2: Capital Asset Pricing Model

Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) is a model that relates the expected return of a security to its systematic risk as measured by beta.

The model assumes that investors ...

• are rational and use portfolio theory to form portfolios
• have homogenous expectations
• can buy and short-sell any asset
• cannot affect security prices
• have the same investment horizon
• pay no taxes and transaction costs
• differ in the coefficient of risk aversion A

We don't need to run the regression, the CAPM theory tells us that the market portfolio is the efficient portfolio.

S&P500 -> close to the market portfolio

Dow Jones -> 30 assets

Weighted by "value of equity" or by "share price" (Dow Jones for simplicity).

Capital Market Line (which used to be the capital allocation line)

• Individuals choose a portfolio on the Capital Market Line (CML).
• The CML connects the risk-free rate with the market portfolio.
• Risk-averse investors hold a larger portion of their assets in the risk-free asset and a smaller portion in the market portfolio.
• Risk-tolerant investors hold a smaller portion of their assets in the risk-free asset and a larger portion in the market portfolio.

Expected Returns of Individual Securities

Secuirty Market Line

The Security Market Line shows the combination of expected returns and betas.

Application: Firm Valuation

The value of an all equity financed firm is the present value of all future free cash flows.

The discount rate E(rE) is also called the cost of equity financing and accounts for the systematic risk of the cash flow stream

The CAPM implies that:

• Every investor holds the market portfolio.
• Firm-specific risk does not a↵ect expected returns because it can be diversified.
• Only systematic risk a↵ects discount rates and thus valuations.
• Betas measure the amount of systematic risk of an asset.

Estimating and Testing the CAPM

“All models are wrong, but some are useful.”

In reality, investors ...

• are not always rational and not all investors use portfolio theory to form portfolios,
• have heterogeneous expectations,
• face borrowing and short-selling constraints and cannot invest freely in all assets,
• can affect security prices,
• have different investment horizons,
• pay taxes and transaction costs.

The alpha of a security is defined as the excess performance above the CAPM implied return; it measures mispricing relative to the CAPM

If the CAPM holds, then ... alpha = 0

Estimating the CAPM

Amazon Example Interpretation:

• The slope is the beta of AMZN: If the excess return of the market increases by 1%, then the excess return of AMZN increases by 1.22%.
• The intercept is the alpha of AMZN: AMZN generated an abnormal excess return of 2.00% per month relative to the CAPM.
• The R^2 is a measure of the fit of the linear regression: 39% of the variation in AMZN is systematic and explained by variation of the market (explained by the model). 61% of the variation in AMZN is firm-specific (not explained by the model).

Mispricing

• alpha > 0: Firm is undervalued. Buy recommendation.
• alpha < 0: Firm is overvalued. Sell recommendation.
• Analysts search for positive alpha assets with fundamental analysis.
• Quants search for positive alpha assets with regression analysis.

Smart Beta Investing

• Starting point: There are too many risky assets to compute the mean-variance frontier.
• Solution: Form portfolios of similar companies, such as value and growth firms (high P/E ratio).
• The idea is that value and growth firms behave very similar in terms of risk and return.
• Smart beta investing portfolios are formed based on companies’ accounting information such as the market equity to book equity ratio.

Styles:

• Value: market-to-book equity, price-earnings ratio, price-dividend ratio
• Size: market equity
• Momentum: prior return
• Risk: beta, total or idiosyncratic return volatility
• Asset growth
• Net share issuance
• Profitability
• Leverage

Value versus Growth Investing

• Firms with a high market to book equity ratio are called growth firms.
• Firms with a low market to book equity ratio are called value firms.

(Redo the ranking and portfolio formation every December.)

Value vs Growth Firms

In the long term, value firms out-perform growth firms.

2010-2021, growth has done significantly better.

Small vs Big Firms

2000-2020, small firms has done better than big firms.

Small Value vs Big Growth Firms

2000-2020, small value firms out-perform big growth firms.

Other Investment Styles

• Value firms have higher returns than growth firms on average.

Why? 2 possible reasons:

• Have value firms have higher average returns than growth firms because they are more risky (beta)? -> more risk
• Alternatively, growth firms could be overvalued (alpha < 0) and value firms be undervalued (alpha > 0) by the market. -> Mispriced
• A similar argument applies for small versus big firms.

Failure of the CAPM

Failure of the CAPM can arise because of:

• Inefficient markets
• Behavioral biases
• Multi-factor models

Efficient Market Hypothesis:

• Efficient Market Hypothesis states that prices of securities fully reflect available information.
  • Weak-form:all information contained in the history; (too weak)
  • Semistrong-form: all publicly-available information; (most people believe)
  • Strong-form: all relevant information including inside information (illegal)
• Investors will spend resources to analyze new information as long as this generates higher investment returns.

Near Efficient Markets - limits to arbitrage * Assume it doesn't cost money to collect information -> this is unrealistic * Suppose it is costly to collect information, can a market be effcient in the semi-strong form? * If all information is in the price, why ever invest in gathering the information? * If no one invests in gathering the information, how would the information to be reflected in the price? * Thus, with costly information collection, we only have near efficient markets.

Rational Theories vs. Behavioral Theories:

• Rational Theories: High expected returns are compensation for bearing risks.
• Behavioral theories:
  • Investors do not always process information correctly.
  • Investors make inconsistent or suboptimal decisions.
  • Result: Mispricing from fair value.

"The investor's chief problem-and even his worst enemy-is likely to be himself."

"Trading Is Hazardous to Your Wealth" -> Frequent Trading leads to poor performance

Gender, Overconfidence (men trade 45% more than women), and Common Stock Investment

Behavioral Bias: Value Premium

• Growth firms have had high past earnings growth rates.
• Investors over-extrapolate high past earnings growth rates into the future.
• Prices of these firms are bid up too high reflecting excessive optimism.
• When growth does not materialize, prices fall so returns are low relative to value firms.
• Value stocks are not fundamentally riskier than growth stocks.

Fama-French Model

The CAPM is a one factor model.

Multi-factor models are linear specifications in factors F1...FN:

Factors

A factor is a variable that a↵ects the expected returns of all assets.

Factors can be:

• Macro variables such as GDP, inflation, etc.
• Portfolios of common assets

Chen-Roll-Ross Model (Using Macro Variables)

5 risk factors:

• IP: % change in industrial production
• EI : % change in expected inflation
• UI : % change in unanticipated inflation
• CG: excess return of long-term corporate bonds over long-term government bonds
• GB: excess return of long-term over short-term government bonds

Fama-French Model (Recent and More Popular)

• The constant alpha captures misvaluation relative to the model.
• The market beta measures systematic market risk.
• The size beta measures systematic risk due to firm size. Small firms have a positive size beta and big firms a negative one.
• The value beta measures systematic risk due to financial distress. Value firms have a positive value beta and growth firms a negative one.

Small firms are riskier than the big firms because they are less diversified.

Value firms are riskier than the growth firms because value firms have lower valuation ratios and are more levered.

Regression to test:

The Fama-French model is rejected if the intercept is statistically di↵erent from zero, i.e., its p-value is less than 5%.

Buffett’s Alpha

• Berkshire Hathaway has realized a Sharpe ratio of 0.79, higher than any other stock or mutual fund with a history of more than 30 years.
• Berkshire has a significant alpha in a CAPM regression.
• However, the alpha becomes insignificant when controlling for additional risk factors.
• Buffett’s returns appear to be neither luck nor magic, but, rather, reward for the use of leverage combined with a focus on cheap, safe, and quality stocks.

Topic 4: Corporate Debt

Bond Market

• Coupon: Promised interest payments paid semi-annual quoted as APR
• Face value (principal): Notional amount used to compute the interest payments
• Maturity date: Final repayment date
• Coupon bonds: Pay face value at maturity and regular interest payments
• Zero-coupon bonds: Pay face value at maturity but no interest payments
• Floating rate bond: Pay face value at maturity and variable coupon

Resources:

https://www.sec.gov/edgar/searchedgar/companysearch.html https://www.wsj.com/market-data/bonds https://www.wsj.com/news/markets/bonds https://www.spglobal.com/marketintelligence/en/campaigns/high-yield-bond https://www.spglobal.com/marketintelligence/en/campaigns/leveraged-loan

Bond Yields

Bond Valuation:

• Afirm has issued a bond with T years maturity and coupon rate c.
• Coupons are paid out semi-annually.
• The face value (principal) is K.
• The value of a bond is:

where y is the bond's yield-to-maturity.

Yield-to-Maturity:

• The yield-to-maturity (YTM) is the discount rate at which the present value of future cash flows from the bond (coupons and principal) is equal to the price of the bond.
• YTM and coupon rates are typically quoted in APR and not in EAR.

• The YTM of a defaultable bond exceeds the expected return of investing in the bond, because the YTM is calculated using the promised cash flow rather than the expected one.

Example:

Credit Risk:

\[y_Corp=y_Treasury+CS\]

CS is the credit spread and reflects compensation for credit risk.

Bond Terminology:

• A bond is selling at a discount if
  • the price is less than the face value
  • yield-to-maturity is greater than its coupon rate
• A bond is selling at premium if
  • the price is greater than the face value
  • yield-to-maturity is less than its coupon rate
• A bond is selling at par (at issuance) if
  • the price is equal to the face value
  • yield-to-maturity is equal to its coupon rate
  • book value = market value
  • yield = coupon rate
• There is an inverse relationship between yields and bond prices.

Corporate Debt

Coupon rate won't change but yield changes over time. When price goes up, yield goes down.

• Public debt
  • A public bond issue is similar to a stock issue.
  • A prospectus or offering memorandum must be produced that describes the details of the offering.
  • Corporate bonds almost always pay coupons semiannually.
  • Indenture: Formal contract between a bond issuer and a trust company.
  • The trust company represents the bondholders and makes sure that the terms of the indenture are enforced. In the case of default, the trust company represents the interests of the bond holders.
  • Bearer bonds: To receive a coupon payment, the holder of a bearer bond must provide explicit proof of ownership by literally clipping a coupon of the bond certicate and remitting it to the paying agent.
  • Registered bonds: The issuer of this type of bond maintains a list of all holders of its bonds. Coupon and principal payments are made only to people on this list.

• Private debt

  • Debt that is not publicly traded.
  • Has the advantage that it avoids the cost of registration but has the disadvantage of being illiquid.
  • Example: Term loans and private placements.
  • Term loan: A bank loan that lasts for a specic term.
  • Typically: Floating (foored), secured, most senior. Sometimes: Amortized.
  • Syndicated bank loan: A single loan that is funded by a group of banks rather than just a single bank.
  • Revolving line of credit: A credit commitment for a specic time period, typically two to three years, which a company can use as needed.

• Unsecured Debt: A type of corporate debt that, in the event of bankruptcy, gives bondholders a claim to only the assets of the rm that are not already pledged as collateral on other debt.

• Notes:
  • A type of unsecured corporate debt
  • Notes typically are coupon bonds with maturities shorter than 10 years.

• Debentures:

  • A type of unsecured corporate debt.
  • Debentures typically have longer maturities than notes.

• Secured Debt: A type of corporate debt in which specic assets are pledged as collateral.

• Mortgage bonds
  • type of secured corporate debt.
  • Real property is pledged as collateral that bondholders have a direct claim to in the event of bankruptcy.
  • All classes of securities are paid from the same cash flow source.
• Asset-backed bonds
  • A type of secured corporate debt.
  • Specific assets are pledged as collateral that bondholders have a direct claim to in the event of bankruptcy.
  • Can be secured by any kind of asset

Seniority:

• A bondholder's priority in claiming assets not already securing other debt.
• Most debenture issues contain clauses restricting the company from issuing new debt with equal or higher priority than existing debt.
• Pari passu: A Latin term meaning without partiality. Generally refers to debt instruments being ranked equally.
• Subordinated debt: Debt that, in the event of a default, has a lower priority claim to the firm's assets than other outstanding debt
• Waterfall Principle: Senior > Junior > Equity

Repayment Provisions:

• Fixed rate bond: A bond issuer typically repays its bonds by making semiannual coupon payments and a principal payment as specied in the bond contract. However, the issuer can:
  • Repurchase a fraction of the outstanding bonds in the market
  • Make a tender oer for the entire issue
• Floating rate notes are bonds that have a variable coupon, equal to a money market reference rate, like LIBOR or federal funds rate, plus a quoted spread. The spread is a rate that remains constant. Almost all floating rate notes have quarterly coupons.

Measurement of Corporate Default Risk

The credit spread is

\[CS≈PD*LGD\]

PD is the probability of default and LGD is loss-given-default

Credit Ratings and Rating Agencies

• For many defaultable instruments, an important indicator of credit quality is the credit rating of the counterparty.
• Credit ratings are provided by major independent credit rating agencies (CRAs) such as Moody's, Standard & Poor's, and FitchRatings
• Issuer Ratings are opinions of the ability of entities to honor senior unsecured nancial obligations and contracts.
• John Moody introduced ratings to the U.S. bond market in 1909 when he published the first debt ratings in his Manual of Railroad Securities.

Rating Scale: Moody's Long-Term Debt Ratings

Rating Scale: Standard & Poor's

Credit Rating

1. Business Profile: Business prole is an indicator for likely variability of performance, competitiveness and long-term viability.
2. Scale: Companies with a larger revenue base exhibit a more enduring ability to weather cyclical fluctuations.
3. Profitability: Prot margin = EBITDA to sales
4. Leverage and Coverage: EBITDA to Interest Expense is an indicator of a company's ability to cover ongoing costs of borrowing; Debt to EBITDA is an indicator of debt serviceability.

5. Financial Policy: Management and board tolerance for nancial risk.

6. For a company that starts with a good credit rating default probabilities tend to increase with time.

7. For a company that starts with a poor credit rating default probabilities tend to decrease with time.

"Default":

• A missed or delayed payment of interest and/or principal
• Bankruptcy, administration, legal receivership, or other legal blocks (perhaps by regulators) to the timely payment of interest and/or principal
• A distressed exchange occurs where
  • the issuer oers debt holders a new security or package of securities that amount to a diminished nancial obligation (such as debt with a lower coupon or par amount, lower seniority, or longer maturity), and
  • the exchange has the eect of allowing the issuer to avoid a bankruptcy or payment default.

Bankruptcy

• When a company goes bankrupt, those that are owed money by the company le claims against the assets of the company.
• Sometimes there is liquidation, the assets are sold by the liquidator and the proceeds are used to meet the claims as far as possible.
• In other cases, there is reorganization in which the creditors agree to a partial payment of their claims.
• The recovery rate for a bond is usually dened as the price of the bond immediately after default as a percent of its face value.

Average Recovery Rates = 1 - LGD (loss given default)

Merton Model of Default

• The T-year probability of default is defined as:

\[PD_T = Pr(V_T < K)\]

• In the limit with an infinite number of binomial trees, the binomial distribution converges to a normal distribution.

Topic 5: Leverage and WACC

Capital Structure

\[Leverage=(Short + Long Term Debt - Cash) / V\]

\[Effective Tax Rate = Federal Tax Expenses / Pretax Income\]

Interest Tax Deduction

Tax Cuts and Jobs Act of 2017:

• The Act lowers the maximum corporate tax rate from 35% to a flat 21% on all profits, the lowest since 1939.
• The Act eliminates the corporate AMT.
• The Act also changes the U.S. corporate tax system from a worldwide to a territorial system.
• The Act limits corporations’ ability to deduct interest expense to 30% of income (EBIT).
• The Act allows companies to repatriate the $2.6 trillion they hold in foreign cash stockpiles. They pay a one-time tax rate of 15.5% on cash and 8% on equipment.

Interest Tax Shield (ITS): The reduction in taxes paid due to the tax deductibility of interest.

\[ITS = Tax Rate * min(Interest Expense, 0.3*EBIT)\]

This benefit is the computed as the present value of the stream of future interest tax shields the firm will receive:

\[V_ITS=PV(ITS)\]

Costs of Bankruptcy and Financial Distress

• With perfect capital markets, the risk of bankruptcy is not a disadvantage of debt, rather bankruptcy shifts the ownership of the firm from equity holders to debt holders without changing the total value available to all investors.
• Direct costs of bankruptcy
  • The bankruptcy process is complex, time-consuming, and costly.
  • Costly outside experts are often hired by the firm to assist with the bankruptcy process.
  • Creditors also incur costs during the bankruptcy process.
  • They may wait several years to receive payment.
  • They may hire their own experts for legal and professional advice.
• Given the direct costs of bankruptcy, firms may avoid filing for bankruptcy by first negotiating directly with creditors. This is called a workout.
• While the indirect costs are difficult to measure accurately, they are often much larger than the direct costs of bankruptcy.
• Indirect costs of bankruptcy:
  • Loss of customers
  • Loss of suppliers
  • Loss of employees
  • Loss of receivables
  • Fire sale of assets
• The average direct costs of bankruptcy are approximately 3% to 4% of the pre-bankruptcy market value of total assets.
• The indirect costs of financial distress may be substantial. It is estimated that the potential loss due to financial distress is 10% to 20% of firm value.

Optimal Capital Structure

• Trade-off theory: The firm picks its capital structure by trading of the benefits of the tax shield from debt against the costs of financial distress and agency costs.
• Key factors determine the costs of financial distress:
  • The probability of financial distress
  • The magnitude of the costs after a firm is in distress
• For low levels of debt, the risk of default remains low and the main e↵ect of an increase in leverage is an increase in the interest tax shield.
• As the level of debt increases, the probability of default increases and the costs of financial distress dominate interest tax shields.

Firm Valuation

The Market Value Balance Sheet Identity

The enterprise value is the present value of after-tax operating free cash flows plus the present value of the tax shields.

WACC

• When interest expense is tax-deductible for a company, debt financing produces tax shields.
• Weighted average cost of capital (WACC): Account for the tax shield by adjusting downward the discount rate used to value the future FCFs.
• Using the perpetual growth method, the enterprise value is:

where r_wacc is the weighted average cost of capital and g the (perpetual) growth rate of FCF.

• r_wacc > g

Effective Corporate Income Tax Rate

\[Effective corporate income tax = Income Tax Expense / Income Before Taxes\]

• When a business occurs operating expenses that exceed its revenues, a net operating loss (NOL) has been created.
• Firms can carry NOL (indefinitely) forward and apply it against any taxable income, which reduces the amount of taxable income in those years.

Two-Stage Valuation for Growth Firms

g1 > g2; r_wacc > g2

Cost of Equity and Debt

Cost of Equity

1. CAPM Model

2. Fama-French Model

Cost of Debt

Credit Rating: http://finra-markets.morningstar.com/MarketData/Default.jsp?sdkVersion=2.61.2

Merton Model of Default Risk

• Consider a one-year bond with yield-to-maturity y. For each $1 invested in the bond today, the issuer promises to pay (1 + y) in one year.
• Suppose the bond will default with probability p, in which case bond holders receive only (1 + y − L), where L is the expected loss per $1 of debt in the event of default.

\[E(rD) = (1 − p)y + p(y − L) = y − pL\]

Corporate Bond Yields:

WACC with Leverage Adjustments

• Leverage increase the Cost of Equity

Problem:

• The goal is to value a private firm.
• To compute the cost of equity, you have to rely on comparable public firms or industry-level firm data.
• In most cases, the capital structure of public firms is different from private firms.

Solution:

1. Compute the unlevered asset beta for the industry or comparable firm.
2. Compute the equity beta for the private firm as a function of its leverage.
3. Use WACC to discount free cash flows.

Harris and Pringle

Beta by Sector (US): http://people.stern.nyu.edu/adamodar/New_Home_Page/datafile/Betas.html

Modigliani and Miller (1963)

• The Modigliani-Miller model assumes that firms never adjust the amount of debt in their capital structures. In contrast, the Harris-Pringle model assumes that firms make constantly adjustments to the capital structure.
• The differences between these formulas are quantitatively insignificant unless leverage is very high.
• What is important is that you understand why di↵erent formulas appear in practice, and the underlying reason for the di↵erences. You can always look up the actual formula.