# Four Axioms of Finance.

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Topic 0: Intro

Four Axioms of Finance: 1. Investors prefer more to less 2. Investors are risk averse (IMPORTANT FOR INVESTOR PREFERENCES) 3. Money paid in the future is worth more than the same amount today 4. Fin. markets are competitive, no arbitrage

Arbitrage Opportunity: Possibility of making money from no money (e.g. borrowing at a risk free rate and buying a risk-free asset with a higher rate of return)

Relevant Statistics

Random Variable: Value representing outcome of an uncertain event. Discreet (e.g. coin flip) or Continuous (e.g. weight, returns)

Distribution: Likelihood of each possible event (e.g. 50% heads, 50% tails for a discreet outcome, normal distribution for continuous outcome). Normal dist.: 68% within 1 SD, 95% within 2 SD

Expected Value (E[Ri]): Avg outcome if an event is repeated infinitely often. Probability-weighted avg of possible outcomes; p(s) = probability of event s happening

[pic 1]

Variance (σ2ι): How much a variable fluctuates around its mean

[pic 2]

Standard Deviation (σi): Sqrt of variance. ALSO KNOWN AS VOLATILITY

Covariance(Cov[Ri,Rj]): Avg. Of the products of their deviations from the mean. Positive if the two random variables tend to be unusually high at the same time, negative if one variable tends to be high when the other is low. The covariance of something with itself is its variance.[pic 3]Solving for CAPM covariance:[pic 4][pic 5]

Correlation(ρij): Always between -1 and +1

To estimate mean, variance and covariance from historical data, use sample counterparts of their definitions:[pic 6]

Portfolio: Combination of N assets, with returns R1, R2,...,RN

Portfolio P has portfolio weights (percentage of wealth invested in asset i) of w1...wN. These weights sum to 1; A negative weight indicates a short position on an asset

Portfolio return is the sum of each asset’s return multiplied by its corresponding portfolio weight; Expected portfolio return substitutes E[R] for R

Portfolio Variance for Two Securities:

[pic 7]

Recall: ρ12•σ2σ2 = covariance(R1,R2)

Portfolio Variance for N Securities:

[pic 8]

Topic 1A: Financial Instruments

Real Assets: Assets used to produce goods and services (PPE, human capital, etc.)

Financial Assets: Claims on real assets (stocks, bonds, derivatives, etc.)

Diversification: Investing across multiple assets (instead of one) to reduce risk

Hedging: Taking an offsetting position in fin mkts to offset given risk

FIXED INCOME SECURITIES: Bonds and borrowing instruments (e.g. treasuries) with FIXED cash flows (e.g. coupons or interest payments). Must be valued using a time value of money (TVM) adjustment. Payment schedule for \$1k, 10 yr, 8% semi annual coupon bond:

[pic 9]

Treasuries: Bills (Maturity under a year), Notes (1-10 yr maturity), Bonds (10-30 yr maturity) w/ semi annual coupon payments

Municipal Bonds: Bonds issued by state & local govts, exempt from federal income tax & state taxes in issuing states (T bills are not exempt from state taxes). General Obligation Bonds are backed by taxation power of the municipality, while Revenue Bonds are issued to finance specific projects (e.g. airports) and are riskier.

Commercial paper: Short term corp loan agreement (30-90 days)

Corporate Bonds: Longer term, typically semi annual coupons, “senior” and “junior” classes of payout order in case of default

EQUITY (STOCK): Ownership in a firm. Dividends are uncertain, indefinite maturity, risky with variable liquidity. Valuation: TVM + RISK ADJUSTMENT

Common Stock: Voting Rights (JR)

Preferred Stock: Non-Voting (SR)

Bankruptcy Payout Order: 1. Govt (IRS) 2. Employees (Wages) 3. Senior Bondholders 4. Junior Bondholders 5. Pref Stockholders 6. Com stockholders

Derivatives: Securities whose cash flows depend on the values of other financial assets, valued at TVM + risk + option adjustment. (e.g. options, futures)

Call Option: Right to buy the underlying asset at a specified price (Strike Price) on a specified date (Maturity) Put Option: Right to sell the underlying asset…

Long Future: Obligation to buy the underlying asset… Short Future: Obligation to sell the underlying asset… (Two kinds of futures: Commodities or financial)

Mutual Fund: Financial intermediary that pools investor funds to buy assets. Offer record keeping/administration, diversification and divisibility, professional management, and lower transaction costs. Compete with ETFs (which trade all day)

Asset-Backed Securities: Bundling of existing securities (mortgages, corporate bonds, credit card receivables), an example of Securitization

Securitization: Creating a security out of an asset that was previously untraded

Topic 1B: Financial Markets

Equilibrium Price: Price at which the supply and demand for something are equivalent

Primary Mkt: Market for new issues of securities. Govt securities typically auctioned, corporate securities typically underwritten by inv. Banks. Uniform Price Sealed Bid Auctions > Multiple Price SBAs; people bid lower when they know they’re paying what they bid.

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