\(\newcommand{\Cov}{\mathrm{Cov}}\)
The notes in this class are for Coursera’s Introduction to Financial Markets taught by Shiller.
Let \(y\) be the rate of return of a stock. Then \(y=\beta x+\alpha\) where \(\beta\) is called the correlation to the market, and \(x\) is the rate of return on the market.
Do not model returns as Gaussians. Real returns have a much fatter tail. The Cauchy distribution has a fat tail. Also, be wary of using the Central Limit Theorem too much. It is wrong if the underlying variables are correlated (often true for stocks). Also, he claims it is wrong for fat tails?
The largest US market drop in a day was 20% (1987).
Do not assume that if you are buying many stocks that you are diversifying and reducing risk. The stocks are not independent/. At least try to gauge their independence from one another. He claims that independence means an average rate of return of 0. The fact that it is not 0 is a clue that there is much dependence.
Insurance has 3 factors:
- Risk pooling
- Moral Hazard: Many act carelessly because they know they have insurance.
- Selection Bias: Only at-risk people sign up, causing the price to increase, and then pricing people out of the market. For insurance to work, many non-at risk people need to buy it.
The average US stock market return from 1802-2012 was 6.6% adjusted for inflation. Government returns in that same period are under 3%. Why did stocks do so much better? Partially this is just selection bias. The US is the most successful capitalist country, and so we should not look at their numbers.
Let the x-axis be the rate of return of the market, and the y-axis be the rate of return of a given stock. Let each point represent a year. The slope of the line is \(\beta\).
The idiosyncratic risk is the risk of the stock that is independent of the market (e.g. Steve Jobs getting sick). People care about systematic risk. The assumption is that idiosyncratic risk averages to 0.
Negative \(\beta\) stocks are good for cushioning against a crash. Gold is often considered a negative \(\beta\) - people tend to want it more when the market is doing poor.
Let \(r_{f}\) be the risk-free rate (e.g. rate of government bonds?)
This equation is used to diversify. A negative \(\beta\) reduces the variance!
A short sale is one where we hold negative quantities of stock. You borrow the shares and sell them. You owe the shares, not the value of the shares. When the price drops, you can easily buy shares cheaply and pay your loan. Not many opt for shorting - the government even put a moratorium on shorts for many companies soon after the 2008 crash.
Say I put \(x\) dollars in a risky asset. Then the expected value of the portfolio would be \(xr_{i}\). The variance would be \(x^{2}\sigma_{r}^{2}\).
Note that this way you can get pretty much any expected return you like. You borrow from a risk-free rate, and invest. The trouble is the variance. Because of the variance, you may lose money. But you can guarantee the expected return!
If you invest in 2 stocks (\(x\) in the first, \(1-x\) in the second, assuming you have only a dollar to invest):
Expected value: \(r=xr_{1}+(1-x)r_{2}\)
Variance: \(x^{2}\sigma_{r_{1}}}^{2}+(1-x)^{2}\sigma_{r_{2}}^{2}+2x(1-x)\textit{Cov}(r_{1},r_{2})\)
So you can reduce variance if you find two stocks with negative covariance.
It is instructive to plot the expected return vs the standard deviation when you have, say, 3 stocks. Very instructive. He showed an example of oil, which is very volatile, and generally a very risky asset. But putting the right amount of oil in your portfolio can actually both increase your expected return, and lower your variance!
Suppose you had an asset, like land. Suppose the first year it yields value of \(x\). Then each year after that, it yields more (by \(g\)) - so the second year it would yield \(x(1+g)\). The third \(x(1+g)^{2}\) and so on. Here the \(g\) is due to more demand, technology, etc. Let’s pretend the rate is fixed and goes on increasing forever.
Let \(r\) be the rate of decline. So the first year the value is \(x/(1+r)\). The second year it is \(x(1+g)/(1+r)^{2}\) and so on. What is the present value of the land? If we sum up the terms, we get \(x/(r-g)\) (only works if \(r>g\)).
BTW, the assumption of \(g\) being constant and accurately estimated has risk. We counter this by increasing \(r\).
Moral: Even a declining business is a good investment if the price is less than the present value! Historically, people always like to go for businesses whose value is increasing. But when that happens, it’s a good time to find declining businesses! Consider railroads - they were big in the 1800’s. But in the 1920’s or 1930’s, everything was about newer modes of transportation (e.g. airplanes) - to the extent that railroad prices dropped like crazy. So they turned out to be a great investment! Look for steady industries that won’t go away, and are not cool (or even anti-cool).
Limited liability: If I own part of a business via shares, I cannot be sued for crimes the business commits. Side effect of this was investor psychology: People started treating it as a worry-free investment, like a lottery. The barrier to buy went down drastically. It made it fun. The other side effect was that it promoted a diversified portfolio. Without it, a diversified portfolio was incredibly risky.
Inflation indexed debt: The idea that a loan should be adjusted for inflation. So if a bond is promising 4%, it should promise it after accounting for inflation. Apparently very rare. And he doesn’t know why.
There is a lot of risk out there that is not managed well - we don’t have insurance for it. There is plenty of room for innovation here. We don’t have good insurance for property values going down. We don’t have good insurance for our job being automated, etc.
In the efficient market hypothesis, the future value of the stock is essentially the result of a random walk - not predictable at all. So the only rational thing to do is a have a full diverse portfolio.
He thinks the market is fairly efficient, but not perfectly so and inefficiencies do crop up. Recommends that if you want to get into investing, it is safer to assume it as a first order, otherwise you get overconfident.
where \(P\) is price and \(E\) is earnings. It is assumed here that earnings is equal to dividends. If \(P/E\) is high, it could be that it is low risk (reflected in \(\beta\)), so people are willing to pay for the stability, or the \(g\) is high. He did not think a \(P/E\) is a good indicator of whether a stock is a good buy or not.
He strongly believes in behavioral finance/economics.
People overestimate the probability of success (or anything that will make them happy). Wishful thinking bias. It explains the volume of trades per day.
Cognitive dissonance: The conflict in your mind when you learn what you believed is wrong.
People who had just bought a car were shown recent car magazines with ads and asked to look at any ad they liked. They had a strong bias to look at ads for the car they bought - they wanted validation for their purchase.
People in a poorly performing fund will hang on in the hope of recovering their losses.
Shefrin & Thaler: We should look at our whole portfolio, not a part of it. But most people have a “safe” part of their portfolio, and a “risky” part of their portfolio. Instead you should look at your whole portfolio and compute the risk/variance/expected return. Isn’t that what will matter in the long run?
Attention anomaly: You cannot pay attention to everything. So you focus on only a small part. Also there is a social basis for attention - we pay more attention to things others are paying attention to.
Anchoring: People anchor stock prices to their recent prices. Or to other stock prices in the same country.
He thinks people should learn more about finance, but just as with medicine, they should still see a doctor. He does acknowledge the issue of untrustworthy advisors.
Compound interest. If \(n\) times a year, the balance is \((1+r/n)^{nt}\) after \(t\) years. With continuous compounding it is \(e^{rt}\).
A discount bound vs coupon bond. A discount bond of $100 is bought for less than $100. The price rises over time to $100.
PDV is present discounted value. PDV of a dollar in years is:
He gave formulas for these:
A consol pays quantity \(x\) forever. A growing consol increases payments by factor \(g\) annually.
- Consol PDV = \(x/e\)
- Growing Consol PDV = \(x/(r-g)\)
- Annuity PDV = \(x\frac{1-1/(1+r)^{T}}{r}\)
A growing consol pays \(x(1+g)^{t-1}\) in time \(t\). An annuity is like a consol but it stops after a while.
Forward rates is taking an interest rate in advance. Example: Suppose in 1925, I know I will have $100 in 1926 to invest. But I want the money back in 1927. How do I do it? Solution: In 1925, buy some number of 2-period discount bond maturing at $100 in 1927. Then in 1925, short one 1-period discount bond maturing at $100 in 1926.
Indexed bonds: Value tied to inflation. Protects from inflation. Most countries don’t have them.
Leveraging means putting more money into something than you have (i.e. you are borrowing money).
China is highly leveraged. The amount of debt exceeds the GDP.
In 2014, in the US:
- Household + nonprofit assets (including shares owned, etc) was $98.3 trillion, with liabilities of $14.2 trillion.
- Corporate equity is only $13.9 trillion. Mutual funds another $7.8 trillion. Pension funds are $20.6 trillion (not counting social security).
- Real estate is $23.7 trillion.
He thinks it is better not to buy a home, but to rent and instead invest in a diverse market - in terms of risk (less risky).
A corporation has a board chaired by the CEO. The board members are elected by shareholders. They then vote for who will be CEO and president.
For profits are owned by shareholders. They exist to benefit the shareholders.
Nonprofits are unowned. It has self-perpetuating directors. Does not pay corporate tax. They do not have a price per share - they don’t exist to benefit shareholders. Their purpose is to serve their charter. Nonprofits can make profits - they just don’t distribute to shareholders.
Splits in shares are pointless. They merely want to target a certain price for psychological reasons.
One buys shares to get dividends. Historically, dividends are more important than the stock price - more returns in the stock market are due to dividends as opposed to share prices.
Companies don’t have to pay dividends. They usually do it as a sign that they have matured. When a company pays dividends, the share price should drop by the amount per share on the ex dividend date.
Common stocks are the usual stocks - dividend is paid at the discretion of firm. Preferred stock has a specified dividend amount. It also does not need to be paid, but a company cannot pay dividends on a common stock until it has paid on the specified stock.
Corporate bonds must be paid.
The basic corporate charter says that all common shareholders are treated equally. All shareholders have one vote? They elect the board that decides amount of dividends, etc. You can also have non-voting shares.
To raise money, corporations can issue new shares. This dilutes existing shares. But the hope is the new money will lead to more profits, etc. Generally, effective corporations will first try to raise money by saving. Then by borrowing. Only then do they give out shares. Giving out shares is rare. RSU’s and stock options are giving out shares, though. When share prices are high, companies really do give out shares. So it’s not clear to what extent they really do give out shares (i.e. ignore this paragraph).
Dividends can be paid with stocks. Not a good idea.
Share repurchase - company loses value, but you now have a bigger share of the company. They do it to get tax benefits. Other reasons too.
Low P/E does not mean the stock is a bargain. It only means that the earnings growth is expected to be low, or that the risk is high. But value investors believe in investing in low P/E’s (or really price per dividend). This is assuming earnings equals dividends.
Don’t put too much value on whether a company pays a dividend or doesn’t. It doesn’t really signal much. A lot of companies just pick a dividend amount to target a price per dividend. Also companies don’t like reducing dividends, so when earnings go up, they increase the amount very gradually so that they have a buffer.
Shiller doesn’t believe heavily in efficient markets. He sees too much irrational behavior.
Benefits of REITs: 95% of income must be paid out.
From 1890 to about 1990, the real value of homes did not change (well, a lot of temporary fluctuations, but overall stayed the same). It rose like crazy after 2000. And is rising again!
If you don’t have short sell a stock, then it is possible for people to artificially drive up the prices up to high levels. It is hard to short a house.