FBE 441 Lecture notes PDF

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Lukas Schmid, entire semester course notes...

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FBE 441: Investments 19/1/21 When is demand high? - Investors expect high CF in future bad times - Prices rise When is supply high? - When investors expect low CFs in future bad times - Prices fall - Rather sell high before prices fall Gordon growth formula: - Price of asset = D / (r-gd) - = dividends / (discount rate-growth rate) Portfolio analysis: - Not a good idea to invest all your savings in one stock Asset pricing models: - Determine what conditions stocks should be priced low, and when they should be priced high Lecture 2 21/1/21 Downturns and risk aversion - Investment decisions are about consequences in bad times - Investors feel the pain of losing more acutely than winning – called risk aversion - Asset prices are the result of asset owners’ preferences Investor preferences - Normative: what people should do - Positive: what they actually do - General and accepted fact: investors dislike risk, and like high payoffs ideally in bad times - Risks vary over time, differ across investors, both institutional and individual - They dislike losing money in bad times Insurance contract is a savings vehicle/investment into health - Bad times = car accident. Buy car insurance - Bad times= earthquake. Buy earthquake insurance - Investors are insurance seekers: they are paid out in bad times - Insurance companies and put option and credit default swap sellers are insurance providers: they pay out in bad times

Institutional investors - Pension funds/retirement assets: they invest for us in saving for retirement - Sovereign wealth funds (SWFs): countries save through SWFs - Foundations and endowments: endowments= university endowments/savings. USC invests that to preserve that wealth for future generation of students - Intermediaries: banks, management firms, insurance companies, financial institutions Individual investors: - Single family offices - Multi-family offices - Rest of us (households) HNWI: High net worth individual (>$1 million in liquid financial assets Mass affluent: >$0.1 million ($100K in liquid financial assets) Values in number increased over time Asset owners and asset managers - They do not manage their investments themselves - They rely on asset managers and asset management companies Asset managers: - Mutual funds: big pools of savings invested in big pool of assets - ETFs - Hedge funds - Private equity - Asset managers charge fees for their services Households - Wealth of all Americans = 125 trillion, liabilities = 16 trillion - Assets = houses, durable goods like cars - Financial assets = 90 trillion Indirectly held stock: retirement account in a pension Equity in noncorporation business: uncle’s business Double hitter: company does bad, you lose your job + if you own stock and stock goes down, then you’re hit hard. In short horizon: - Make sure you have liquid assets so that you can convert to cash quickly in case of emergencies Long horizon: - In case of inflation, in terms of purchasing power, your savings evaporate quickly

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Mean reversion: stock market valuations are the highest right now. They might come back to previous levels. Longer you wait, prices will fall more. This means it will come back to pre-levels.

Agency bonds: lending to housing institutions Indirect investments: pension fund will be invested in stock -

Truck drivers should buy TSLA (TSLA pays off when truck drivers are displaced by technology. This is displacement insurance) Software engineers should not invest

Pension funds - Defined benefit vs defined contribution - CalPERS: after retirement you’re paid out a fixed amount - Benefit factor x highest pays over the last 3 years * # years in service - Eg: teacher retiring at the age of 55 has a benefit factor of 2%. This is a replacement rate of roughly 0.02 * 30 – 60% - Riskless income stream in retirement Defined contribution: - Fixed contribution by employer, investment in variety of assets - Employer chooses a set of funds, employee the particular investment Endowments - Universities have lots of savings: Harvard has of $40 billion - Make sure it pays out 4-5% a year to help support day to day activities of college Foundations: - Pool of wealth from different investors SWF: - Funds that invest in nations - National resource is oil in these countries 26/1/21 Lecture 3: Trading in financial markets Primary markets - Where securities are initially issued - Issuers sell to investors - Entities need funding, and to obtain funding, they issue securities. Can be companies, government or individuals - Companies sell stock to investors - Government sells bonds to investors

Secondary markets - Security trading after issuance - Investors sell to investors Primary market - Purpose: raising funds - Issuing company seeks advice from investment banks - Investment bank provides various services o Legal counsel o Capital commitment and marketing o Secondary market liquidity o Absorb initial shares and sell them to investors o Investment banks help companies raise funds, tries to find investors that are willing to buy shares in a company that is looking for financing. IB convince investors to commit capital and buy shares of this company. IB finds investors willing to contribute $ in shares financing. Then, IB pays that $ to company, and buys those shares. IB owns shares, they have to sell these shares to investors. o This process called book building o But if this company goes bad, IB can’t sell companies shares to investors, so IB is putting themselves at risk, so to compensate, IB charges fees. That’s how IB makes money o Then, secondary market trading starts - At the end of the process, equity shares (stocks) are issued to investors - 2 types: o Initial public offering  When company goes public  You allow investors to buy shares, so the company gives up some ownership rights. o Seasoned equity offering  When company needs funding, it raises equity financing  Company sells more shares to public, then my existing stake in company gets diluted  Delusion of initial owners claims IPO performance on first day - Commit to buy shares to IB. you buy in morning and sell in evening - In US, there’s 20% ipo returns - IB sold shares to initial investors at too low a price relative to what market was willing to pay for a stock (as a result, trading prices on 1st day go up) - IB would incentivize investors to buy shares by placing low price- they would buy low. Over course of first day of trading, prices went up. Secondary Markets

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Most trading takes place here, when investors trade securities among each other in various forms and orgs Investors trade to “buy low, sell high” o Speculate (take advantage of favourable prices). You think prices are too low, so you buy. Think they’re high, then sell o Hedge (save for bad times): hedge/protect yourself by trading in secondary markets o Trading opportunities arise because diff investors have diff investment and hedging needs (heterogeneity) o If Issuers are minimally involved in secondary markets o Share buybacks: buy back their shares. They might have sufficient funding internally. Makes shareholders better off o Current prices inform companies about how their plans are perceived by investors

Trading Assets - Financial institutions/intermediaries facilitate trading in secondary markets - Brokers o Facilitate contact between buyers and sellers o Real estate market o Brokerage fees - Dealers o Hold inventories of assets, ready to buy/sell them o Provide liquidity to markets o Charge fees for these services because they hold the stocks and its risky - Many banks/financial institutions provide both brokerage and dealer services (brokerdealer) - Organised exchanges provide trading platforms o Trading floors o Electronic exchanges (ECN) o Recent developments: public vs private exchanges like dark pools, high frequency traders use algorithms to trade fast - OTC markets o Bilateral trade between market participants like dealers, increasingly using their own networks

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Stocks trade on centralised exchanges, corporate bonds trade on decentralized (OTC) markets Prices are quoted in central limit order book (CLOB)

Bid and ask prices - Bid price: price at which investor can sell. Dealer bids at this price

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Ask: dealer asks for price. Price at which investors can buy In general, bidmarket price. Doesn’t make sense to exercise option. So, don’t buy this stock, buy it in open market. Payoff to option is 0.

Example: - AAPL call with maturity date March 18. Stock closes at $106.84 on that day. For an option that’s exercised at maturity: strike price is $90 o Strike price Is lower, hence exercise the option because you will make a profit/payoff of $16.84 o If strike price of 120, then it wouldn’t make sense to buy the option o If stock price goes up sufficiently quickly, then you think about buying it, long it Call option vs long position - Call on AAPL matures march 25 with strike $115, trades at $7. The current stock price is $106.84. exercise decision at maturity. - What is total profit from purchasing call if AAPL closes at 145 on march 25 - What is rate of return on call o Buy 1 call: o Profit: 145-115= 30-7= 23 ($7 paid for the right to exercise the option) o Return: payoff/price – 1 = $30/$7 -1 = 328.57% - How does return compare to taking a long position (assuming no dividends) o Long 1 stock: o Return: 145/106.84 – 1 = 35.72% buying option magnified return on apple by factor of 10. - What if stock closes at $110 on March 25? o If S_T = $110, option won’t be exercised. Max (110-115.0,0) = $0. So, return = -100% o Long: 110/106.84 = 2.96% - Taking call position on Apple magnifies the upside and downside. Hence called leverage position on the stock Put option - Put gives right, not obligation to sell underlying asset/stock at pre-specified price, strike price K o At maturity date T if option is European o This is when you think stock will lose value, so you’ll get protection of losses on stock by selling it at price K o Anytime until maturity date T if option is American o Payoff: max(K – P_T, 0). 0 is not exercised

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Sell stock at higher price than K means you wouldn’t exercise the option bc you would make more money selling at market price If market price at T is lower than strike price, then better off selling at K. you’ll make a profit. Sale price - market price = profit If market price greater than strike, then profit = 0

Example - Buy apple put with mature date March 18. Stock closes at $106.84. - What is payoff if strike price is $90 o Have the right to sell apple at $90. But doesn’t make sense because stock price is 106, so we would want to sell at 106. Payoff at T = 0 - What if strike price is 120? o On march 18 we can sell put at 120, instead of selling at market price of 106. Payoff = 120-106.84 = $13.16 - Protect yourself against losses by doing put options Put option payoff vs short position - Put on apple that matures march 25. Strike price=115, trades at 17. Current stock price is 106.84. - What is total profit from purchasing If apple closes at $90 on march 25? o Paid 17 to get put, payoff = strike price-closing price. $115-90 = 25 o So, -17 + (115-90) = $8 o Return = 25/17 – 1 = 47.06% o Protects you against movements if stock price falls below $115 - Stock price closes at 135 or 145 on march 25. o Payoff = 0, return is -100% because you will not exe rise. Loss will be $17 o Beyond 115, no further losses from stock price increase. The short position will keep losing as the price appreciates. o 106.84-135 = $-28.16 o 106.84-145= $-38.16 o So in put position, you are insured of these losses, so put options give you insurance Long = buying stock and selling it later Call = magnifies the exposure In the money, at the money, out of the money - ITM: option would have positive payoff if exercised right now o Call option, strike lower than stock price, exercise the option bc you will get profit. So, the option is ITM - ATM: strike equal to current underlying price o Doesn’t matter if you exercise or not. Payoff = 0 - OTM: option not exercised right now

o Strike price500 at maturity and you really think it’s worth paying the extra right now for higher returns at maturity - Compute rates of return for these strategies where TSLA trades at 400, 500, 600 and 700

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Suppose you go long, and in nov 20 tesla has fallen to 400. If you take long position, you make a loss of (400-440=$40). Return = -9% ITM option: strike price of 410. You wouldn’t exercise option because it’s cheaper to buy 400 in market than 410. But you paid $90 for it, so loss is 90= -100%. Stock price is 700, then you are better off OTM call at 500, costs you 58, but you make profit of 200, and return of 244. This is a leveraged position. Magnifies downside and upside.

Index puts - Would you expect the average rate of return on purchasing ATM and OTM put options on the sp 500 INDEX TO BE POSITIVE OR NEGATIVE? WHY? - Index outs protect you against large downside movements in indices. - You can buy index puts from banks at some price. - Average returns/expected returns on index put- instrument that protects you on from stock market crashes because your losses are bounded by strike price.

PutWrite index: hypothetical portfolio that sells ATM 1-month SP 500 put options and invests in T bills - Average returns on buying index returns is negative. Make losses. Selling index puts makes money, profitable. - They protect you against losses, so it gives you insurance in stock market crashes. But someone has to sell you the insurance, so if you buy any kind of insurance, on average you’ll make losses on it because you pay insurance premiums. And when you end up getting sick, you benefit from the insurance. Average returns from buying insurance are always negative. Selling insurance is always positive because it’s risky. Put options: example - Gives the right to sell security at prespecified price - Stock price = 100, strike price = 95, put option price P=1, 1 month maturity - S=90, put payoff 5 (sell at 95, Stock price at 90). Returns = 400%, stock return = -10% - S=100, put payoff = 0, so don’t exercise. Returns = -100%. - S=110, put payoff 0, so don’t exercise - When market goes down, you make money - Expected returns from buying puts are negative eon average Put options returns - Most of the times, OTM returns are -100% - Only during stock market crashes, returns go up. - As insurance seller you make positive returns during market crashes Example: variance swaps and COVID - Variance swap is a contract that has high returns when volatility is high. That’s when you want to have insurance. Average return on variance swaps is negative - Contract where buyer pays the price and gets the sum of squared daily returns over the next month as payoff - So, the payoff and realized return is higher when volatility is high 18/2/21 Review for Exam -

75 minutes Open book Simple calculations. Have excel/calculator/phone

1. Square inc is trading at 112.26 per share on sept 19 2019. Company has 321.29 milion shares outstanding. What is market capitalisation? - 112.26*321.29million = $41.7 billion

2. Investor is forced to take either opportunity A or B. both A and B have expected return of 5%. A’s return volatility is 15%. B’s return volatility is 25%. Does investor have a strict preference between the 2? a. Riskier opportunities have higher avg returns. Lesser risk, better for investors. b. So, they would pick A c. Yes, fixing expected return, risk averse agents prefer lower volatility 3. Investor is choosing a portfolio allocation between riskless T-bills and a stock market index fund. Would she choose to invest her entire wealth in T-bills? a. No because diversification is required. Risk averse investors have preference for low risk, but they will accept the risk with high expected returns b. 7% equity risk premium, Sharpe ratio = 0.4 4. Your deposit $2500 of own funds into a margin account with the intention of buying XYZ shares, which is currently selling for $100/share. - How many shares can you purchase given an initial margin requirement of 50%? a. =equity has to be 50%, so $5000 worth of shares. b. so 2*2500 divided by 100 = 50 shares c. leverage ratio = 50%. 50% of funds are borrowed from broker - if stock falls, leverage rises because you’re more at risk for default 5.

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If you bump into margin requirement and you get margin call, you might have to sell shares to get the margin. When share price falls, debt in position doesn’t change. You still owe broker 2500. Value of position declines to $3500, because 50 shares*$70. So, equity = 3500-2500 = $1000 Margin requirement is at least 40% of assets. 1000/0.4=2500= maximum allowed assets, but you have 3500. So, it means you have to get rid of excess $1000 worth assets Equity should be greater than 0.4* assets Assets should be < Equity/0.4 So, you sell $1000 worth of shares, so $1000/70=14.286 shares=15 shares

6. Order books

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WHAT WOULD BE TOTAL AMOUNT PAID BY A TRADER WHO PLACED A MARKET ORDER TO BUY 400 SHARES? o Because you’re a trader, look at ask side. Market order, buy at best price o 300*3.46+100*3.55= $1393 o Now, at 3.55 there are 400 shares left. The shares at 3.46 are gone from order book What would order book become if you submitted a limit sell order for 400 shares at a price of 3.45? o It wouldn’t go through because there’s no bids at that price. You can only sell at 3.44, but you want to sell at 3.45. so, order cannot be filled. So, order goes into order book, on the ask side because you’re putting it up as a sell order. You’re willing to sell at3.45 means someone can buy at 3.45, so it goes on ask side.

What would order book become of you instead submitted a limit sell order for 400 shares at 3.44? - Order would go through, bid side would have 1100 shares left

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There is a buyer at $3.44 so order gets executed Selling pressure is higher than buying pressure, so it drives down price overtime. Execute 1100, then best price is 3.42, so you can buy at cheaper price in future.

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((17*121+45*98)+3400) = $9867 NAV/share = 9867/15 = 657.8

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the probability of observing a daily return that is more than two standard deviations higher than the mean is 2.5%. ratio: fee revenue/assets under management. AUM= NAV

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of whole fund $50/9867 = 0.5%

8. Returns

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Stock A: ((111+4)/100)-1

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15%, 7%, -44%

9. Returns: what were equally rated and value rated annual return

Value rated:

(15+7-44)/3 = -7.333

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Take share price of 2014

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The losses from C is less in terms of proportion

10. Normal distribution - How well does normal distribution fit daily US stock market returns o Almost normal day to day but there are some rare negative events, some outliers like covid, black Monday. Daily returns are highly non-normal - How stop orders and margin calls could contribute to violations of normality in daily returns o Lots of stop orders in palce, it triggers additional selling o Lot sof leverage position

11. Compounding returns

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12. Options 13.

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Strike < closing price, so because it’s a call, we want to buy it. Current Market Price is above strike price, so it’s a good call option, so we exercise it. Payoff is $15 (140-125). Profit is 15-10. Rate of return = payoff/price -1 = 15/10 – 1 = 50%1

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23/2/21- Problem Set Answers 1. You deposited 100K in margin account and proceeded to buy 150k of stock in GRPN. There is a 30% maintenance margin required by your broker. a. Size of margin call if price of GRPN falls by 60%? - Asset = 150k. debt = 50K. equity = 100K - New asset base = 60K (0.4*150K). debt = 50K. equity = 10K - Required equity = 0.3*60000 (30% of assets) = 18K - Margin call = 18K-10K = 8...