Investments Lecture 1 Lawrence Hsiao Logistics Midterm (4/10): 50% Final (6/5):50% Class participation (roll calls; answering questions) Office hour: by appointment Textbook: Zvi Bodie, Alex Kane, and Alan J. Marcus, Essentials of Investments, Twelfth Edition, McGraw-Hill Education, New York, NY, U.S.A., 2021. Introduction Investment: You sacrifice something of value now, expecting to benefit from that sacrifice later. Example 1: An individual might purchase shares of stock anticipating that the future proceeds from the shares will justify both the time that her money is tied up as well as the risk of the investment. Example 2: The time you will spend on this course is also an investment. Return, Risk, and Arbitrage Return Definition: the profit on an investment. Typically measured as a percentage of the amount invested. Example: You buy an asset for $100 and sell it for $150 after a year. ⚫ Your profit is $150-$100 = $50. ⚫ Your return (in percentage) is (150-100)/100 = 50%. Risk Definition: the chance that an investment's actual return will differ from what is expected. (uncertainty in receiving your return) Example 1: You invest in an asset for $100. The value of the asset will fall in [50,250] after a year. Example 2: You invest in cryptocurrencies on a CEX. There’s a chance that it will collapse and you get nothing back. Risk Example: You invest in an asset (A, B, or C) for $100. A. The value of the asset A will be $150 after a year. B. The value of the asset B will be either $50 (probability=0.5) or $250 (probability=0.5). C. The value of the asset will be either $40 (probability=0.5) or $260 (probability=0.5). Which one do you prefer? Why? Please discuss. Relation between Risk and Expected Return • High risk → High future returns • Ex: The expected return in the stock market is higher than the risk-free rate. • Ex: The expected return in the crypto market is higher than that in the stock market. • Why is crypto investing highly risky? Frequency of distribution of annual returns on stocks • Source: Kraken Intelligence Arbitrage • Definition: Taking advantage of price differences across markets to make profits. • Example 1: BTC is priced higher on Binance while lower on Kraken. →Buy BTC on Kraken and sell it on Binance. (Ignore transaction costs) • Example 2: A combo (Burger + coke) is priced at 10 in City A. In City B, burger price is $8 and coke price is $3. → Buy the combo in City A and sell in City B. (Ignore transaction costs) Arbitrage is difficult to sustain • Example 1: BTC is priced higher on Binance while lower on Kraken. → Buy BTC on Kraken and sell it on Binance. → Supply on Binance increases, price decreases → In equilibrium, BTC price on Binance = BTC price on Kraken • Same logic for Example 2 Risk and Expected Return • Two asset: asset A (low risk) and asset B (high risk) Claim: On average, asset B should have higher expected return. (High risk → high expected return) • Suppose not, then arbitrage occurs. All investors buy asset A (pushing up the current price of A) and sell asset B (driving down the current price of B). • Zero-cost arbitrage strategy: Borrow asset B from John (who holds asset B). Sell asset B to get money. Buy asset A, get your high returns in the next period. Buy asset B and repay it to John + some interests. • Limits to arbitrage: short-sale constraints, upfront collateral, time-varying risk, etc. Risk aversion Example: You invest in an asset (A, B) for $100. A. The value of the asset A will be $X after a year. B. The value of the asset B will be either $50 (probability=0.5) or $250 (probability=0.5). A or B? • X = 150, pick A. • What X will make A and B look equally attractive to you? Risk aversion • The tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. • Most people are risk-averse. Topics • Risk, Returns and the Historical Record (Chapter 5) • CAPM and Arbitrage Pricing Theory (Chapter 7) • Efficient Diversification (Chapter 6) • The Efficient Market Hypothesis (Chapter 8) Topics • Debt Securities (Chapter 10, Chapter 11) • Evaluating Investment Performance (Chapter 18) • Special topics: Cryptos, latest work in asset pricing, Behavioral Finance and Technical Analysis (Chapter 9) Asset classes 1. Stock: • dividend • stock price variation • a fraction of ownership of the firm (voting right for example) 2. Bond: • coupon • bond price variation 3. Options and derivatives: • Price variation • An option/obligation to buy/sell/receive/deliver the underlying instrument at/before/after a given time Chapter 5 Rates of Return • Holding-period return (HPR): HPR = (Ending price – Beginning price + Cash dividend) / Beginning price • Returns over multiple periods • Conventions for annualizing rates of return (ignoring compounding) ✓Annual percentage rate (APR) = Per-period rate * Periods per year (n) ✓Effective annual rate (EAR) = (1+APR/n)^n - 1 Inflation and the real rate of interest
