Portfolio Management - Real assets: buildings, machinery, knowledge, research, human capital - Financial assets: stocks, bonds derivatives Real assets create income financial assets are claims on the (future) income from real assets. Your financial asset is another persons (or corporations) = liability (responsabilità, debito, obbligazione). When aggregating the financial assets will cancel out and we thus have: Assets + Liabilities = Real assets • • • Bonds: As a bond issuer (borrower) you are obligated to pay one or more (fixed or floating) payments in the future to the owner (lender). The owner can sell this privilege to a third party. These are considered 'safe' investments. Bonds have seniority under bankruptcy. Stock: A stock is a claim on the future profits of a private company. There is limited liability up to the price you bought the stock for. Considered a 'risky' investment. Derivatives: A claim whose value depends on the value of another financial asset -> A side bet. Sidenote: Limited Liability - Denmark: Interessent/Kommanditselskaber (I/S, K/S (as opposed A/S=LLC)). 100% liability, but no required minimum levels of equity to incorporate and losses and investments are tax deductible. 'Skibsanparter' from the 90's are examples of a K/S. - English law did not permit LL until the Limited Liability Act of 1855. Before that (almost) exclusively full liability was the norm. First step towards LL act was capping the loss: Ex: Buy one share for 100 pounds - liability is max 1000 pounds Fully limited liability was seen as suspicious since it removed some of the stockholder incentive for monitoring the management as well as the creditworthiness of the other owners. Stock emissions was therefore a much more credible signal of credit quality than it is today. Bank crisis in London 1866 (Overend, Gurney & Co.) led to massive losses and risky capital dried up. LL became popular because it was a way of inducing investors to enter the market. Other countries then followed suit. Stock dividends Irrelevant under classical capital structure theory. - Advantages: Argument 1: “A bird in the hand...” argument, Argument 2: lower taxation until early 2013 in the USA. - Disadvantages: Paying a dividend is equal to a forced realization of your investment. You cannot time your realization so you offset gains with losses. Furthermore, in the US: Even if the timing of the dividend payment matches a realized loss you still (almost, pension savings are exempt) always pay taxes on the dividend. (At least the deduction is limited up to 3000 USD, in the US) Regardless of whether your entire portfolio has a net loss. This is not the case for capital gains taxes which are paid for the gains in portfolio in aggregate. Losses may cancel out gains and diminish your tax burden. But how do you pay back money to investors then? Article (Steve Jobs wouldn’t have paid a dividend) argues that share buybacks are better than dividends since they allow you to cancel out the gain with your losses -share buybacks also nicely push up the stock price - but what happens if you stop? (See tech stocks right now) Dividend puzzle: How can we explain dividends? Seen as signal to investors, investors are irrational. Financial stock - Preferred stock: no voting rights, but senior to common stock in bankruptcy. Analogous to a 'perpetual bond'. A way to not give away control (especially in family-owned companies) - Hybrids: Convertible bonds (they convert into equity if something happens), CoCo bonds etc. Financial Market mechanism Capital Supply: Savings, pensions; Investments. Capital Demands: Individual, companies, governments. The role of financial markets is to allocate capital - bring agents in the economy together in equilibrium (supply=demand) What is the price then? Whatever equilibrates the market. Price = (Present) Fundamental Value + Speculative Value Two examples (2 extremes). - A fixed coupon government bond. Cash-flow stream is (almost) 100% predictable. Fundamental Value dominates. - Non-Fungible Token. Zero (pecuniary) fundamental value. Speculative Value dominates. It does not have to be either or see Facebook, Tesla etc. Financial intermediaries Investment Banks: Works as the middleman between governments and companies and the financial markets. For example, by assisting the issuance of bonds and stock or mergers and acquisitions. Very profitable, but perhaps not sustainable. Examples: - Initial Public Offering (IPO) o Consortium of investment banks create a market for the issuing company stock by performing so called 'Road shows'. Trips to potential investors. o A complex game exists between the investor, the issuer and the banks in between, this is very expensive. You pay for the bank to create the market for your stock. Rules apply, like lock-up periods. - Alternatives to IPO o Direct listing: You go the exchange and put your shares up for sale. No new shares are created (recent examples, Spotify, Slack). Cheaper, no lockup period. Arguably riskier. o SPAC: You IPO a buyout company, that has intention of buying an existing private company. The target private company is taken public *automatically* - does not pay for the IPO. (Used often in Private Equity sector). Others type: Mutual Funds - Hedge funds - Private equity - Commercial banks - Mortgage Institutions - Pension funds – Exchanges. Trading with financial assets (US centric) - Non-organized trading, over-the-counter (OTC). Often derivatives. Especially interest rate derivatives are traded this way. Requires only registration with SEC. Dodd-Frank (US) and Mid (EU) legislation has forced a large share of the market to be traded on exchanges or to use central clearing. - Organized exchanges, NYSE. In the past a specialist executes the trade and guarantees a certain market depth. Everything was changed by liberalization of exchanges in 2005. - Electronic trading. Now most trades are eventually executed electronically a broker/dealer (like say, KCG (former GETCO)) makes the market for you by placing the order at one or more - electronic exchanges. But larger trades are done with some human involvement, and of course a lot is still done OTC. Robinhood App. etc. No fees! Your order flow information is more valuable than the fee. They sell this information high-frequency traders. Retail investors = not informed traders. Less risk than taking order from professional. HFT (High Frequency Trading) The Flash Crash: On May 6th 2010 14:45 the DJIA index, fell 9 pct, while recovering most of its value in the following 15 min (See next slide). The crash is believed to be cause or at least exacerbated by algorithms set to buy and sell stocks with very high frequency. Often many hundred times within a single second! Algorithms are based on complicated models to predict and 'manipulate' the price within small time intervals. Trades are executed by broker/dealers, banks, proprietary traders, via the organized exchanges or in OTC 'Dark Pools' (the size of your order is secret within the pool') administered by banks or broker/dealers (this where Robinhood trades are executed). Manipulation is a gray area: In 2015 N.S. Sarao, A London Based HFT was accused of 'spoong' and 'layering' by putting out sell orders he never intended to executed which seems to have partly caused the ash crash. About 20000 financial companies trade US equites. 2% of them account for 73% of the volume! HFT makes a market for more long-term investors (position takers/informed traders). As long as there is a balance between buy and sell orders the HF trader can make money on minimal spreads by predicting the price (often through unfair advantages see the movie the Hummingbird Project). If there is an imbalance they disappear from the market altogether Flash Crash. Lots of solutions have been proposed. 'Circuit breakers' stopping all trading if DJIA falls by a certain pct. Algorithmic/HFT trading remains a controversial issue: - Pro HFT - argument is that they create liquidity. Spreads have gone down significantly since the introduction in 2000. - Skeptics say it increases volatility and is a tax on less sophisticated investors. Trading other financial assets Commodities like frozen orange juice, pork bellies, oil, and derivatives are traded mostly in organized exchanges. Interest rate derivatives like swaps, forwards, caps, floors, credit derivatives like CDS's og CDO's are traded mostly OTC but legislation is forcing a lot of standardized contracts (swaps in particular) to be centrally cleared. Post financial crisis, central 'clearing' is a highly debated topic. Central clearing works by having a 'clearinghouse' putting seller and buyer together. Clearing house takes on the counterparty risk against the posting of margin/collateral. Controversy: Does central clearing reduce or increase systemic risk? General investment theory - Time = Money One € in a year is worth less than one € today (with positive interest rates); - No Risk → No (excess) return; - Diversification: Spread your risk! (don’t put all your eggs in the same basket). The investment decision - Start with Asset Allocation: Stocks, bonds, lottery tickets etc.? What do I want in my portfolio? Depends on risk aversion and time horizon (Top-Down approach). - Next step security selection: Which stocks? Which bonds? etc. In practice people (individuals) don’t do that: most people prefer a bottom-up approach: - Bad Bottom-up approach: 'I like Enron stock because that’s where I work' - Better Bottom-up strategy: 'I read all about Tesla and believe in their business model. Why don’t I place a small fraction of my portfolio in that company' For long term investing: always apply a top down strategy! Side note: In reality no one does this. A study by Rangvid et.al (2017) shows that 1 in 6 of danes own shares. And on average they have 8% of their wealth invested in it. But the majority have invested in only 1 or 2 Danish companies! The efficient Market Hypothesis (EMH) Definition Fama (1970): The Market is efficient if its prices reflect all available information. Important Implications: Unless you have inside information the best estimate of the price tomorrow is the price today (adjusted for risk). The price reacts to new public information immediately. I.e. the price will reflect all available information today to form an unbiased expectation about the future value plus time-value of money (interest rates), etc. => only new information moves the price, new information is unpredictable (by definition) i.e. like trying to predict a coin toss. Cannot predict the market? Avoid active portfolio management (that is their business model). Transaction cost means you will be throwing money out of the window. EMH is controversial: The implication is that Hedge Funds, stock analysts, investment gurus are selling you nothing of value. Is the market efficient? Empirical Evidence from the last 100 years (short answer - will elaborate in the course) - If you mean that there is no free lunch - probably(ish) - If you mean that market value equals "fundamental value" then probably not(ish) Buying on margin Exchanges often allow investors to buy financial assets using borrowed funds - on margin. You are borrowing money to invest: of course, you are paying interest. Margin is the amount that the investor contributes with himself the rest is borrowed from the broker/dealer. You pay interest of course on this. It is denoted as a fraction of the total investment. In the US Federal Reserve dictates an initial margin of minimum 50%. But the price is allowed to drop down to so called maintenance margin which is 30%. If the price drops further you will get a Margin Call. If you don’t increase the margin your position will be liquidated. Student problem: How low can the price go at time 1 before your account falls below the maintenance margin of 30%? Same question but assume instead you pay 2% interest on what you borrow from time 0 to time 1. Short sale To 'go short' - making money when the stock price drops - You borrow the stock from a broker, sell it, and buy it back and hand it back to your broker. - If the sales price is higher than the buy price you earn a profit. - The broker has an inventory of stocks, held as a service to clients who have bought the share. - As a short seller you get to borrow it sell it and buy it back - for a (sometimes substantial) fee. - You can borrow it as long as the original owners don’t want it back. - If the original owner needs it you have to immediately return it. This means that short positions may be cancelled without notice - also referred to as recall-risk or buy-in risk. 'Naked' shorting. To short without actually borrowing the share. Illegal! Legal Naked shorting is typically done via a derivative contract like a contract for difference (CFD) or Forward/Futures. *Essentially* a derivative contract that is entered into at time t=0, and pays (P0−P1), at time 1. Notice that you can in fact have more short positions that than the number of outstanding shares since a stock can be shorted multiple times. I.e borrow it from A, sell it to B. Borrow it from B, sell it to C. One share, but you have 3 long positions and 2 short positions associated with it. Ethic in shorting a stock Empirical studies show that stocks with short sale restrictions underperform compared to peers. A broad investigation concluded that even illegal naked shorting with Failure-to-Deliver events, caused no serious disruption to markets. Economic arguments can be made against short sale restrictions since they hinder proper price discovery and inflates stock prices. BKM cap 5: RETURNS Mean and variance on the price distribution are not meaningful measures because they will be level dependent and hence cannot be compared across assets. - Example: Berkshire Hathaway trades at almost 406,000 USD/share whereas IBM trades at 118 USD/share. If the standard deviation of the price is 406,000/121=3440 times as large for Berkshire Hathaway this says nothing about the risk of Berkshire Hathaway vis-a-vis IBM. Describing uncertainty in investments is always in terms of its return. VERY IMPORTANT SLIDE Return on a zero-coupon bond A zero-coupon bond is a bond with only 1 payment at maturity. The price of a zero coupon bond expiring at in T at time zero is called P(0,T). The value at expiry we can standardize to 100 kr. so P(T,T) = 100 Semantic Side note: Returns and Return rates Computing returns B is better. Annualization of returns Multiperiod return Arithmetic Average return Geometric Average Return The Risk-Free Return Returns on a portfolio of stocks Stock indices Value weighted indices Does not depend on price level. Unaffected by splits but not dividends. The S& P 500 is not a total-return index. If you invest in the 500 companies you also get the dividends. Use the SPTR instead. Many people have drawn wrong conclusions if you forget dividends Divisor d(t) is similarly adjusted in the event of inclusion and exclusion. High turnover of membership, hard to replicate. But better diversified. All the big indices have ETFs that track them. These are traded directly on the stock exchange so you don’t have to manage a portfolio of 500 shares. But you get the dividends if you invest in the funds that track them. Probability Theory: discrete stochastic variables Mean and variance: discrete distributions Conditional probabilities Continuous stochastic variables Formulas for mean and variance Standard deviation Normal distribution Do not put the variance, we need the standard deviation. True = distribution function. Quantiles Example 1: Example 2: Rewriting to the standard normal distribution EXERCISE: Performance measurement If everything else is equal, as investor I want the one with higher sharp ratio. Alternative risk measures VaR for the normal distribution Direct estimators for VaR and ES (expected shortfall) Back testing Value-at-Risk Lower partial Standard Deviation Performance measurement Example: Returns in normal distribution Conclusion: normal distribution is more suited for log-returns than discrete returns. We will still use it for discrete returns due since: Discrete returns are easier to work with for portfolios - the decomposition in (29) is NOT possible using log-returns. The assumption that losses bigger than 100% can occur while unrealistic is a conservative one. Skewness Kurtosis
