Ec 70 - Midterm 2 Key Terms
why are corporate bonds risky investments if (a) held to maturity (b) sell before maturity
(a) if held to maturity, chance of default (default risk) (b) if sell before, yield change as a result of a bad financial event could result in drop in the price of the bond, so you actually lose money
financial history of stock return
*long run* R approx. 7% D/P approx. 4.5% = return from income 2/3 average G approx. 2.5% = return from growth 1/3 *21st century* D/P closer to 2% meaning: less income coming out of stocks because you are buying them at high prices relative to the dividends you get
managing risk to stay in the game
-- it is important to manange your risky portfolio so that if you lose money, 1) you are not miserable with anxiety 2) you do not panic and sell your entire risky portfolio this requires 1) understand the risk up front 2) understand your own tolerance for risk 3) use a disciplined investing approach that will constrain impulsive decisions
an equal weighted portfolio of independent risk assets
0.25 two bad, 0.25 two good, 0.5 one bad one good Mean return of portfolio is unchanged at 5% Variance is now 0.011 - half of what it was before GREAT NEWS! risk reduction in your portfolio --> since variance is half as big now, we should invest double the amount as before
stock breakdown
1. common/preferred 2. large cap / mid-cap / small-cap - size thought of as the total market value of all the stocks listed by the company, referred to as capitalization or cap 3. growth/value - growth stocks have high market values relative to certain accounting measure of the company (optimistic about their potential for future) - value stocks have a lot of stuff accountants find valuable (physical stocks) but market value is low
how to diversify
1. invest across multiple asset classes, including at least bonds, domestic equity, and foreign equity 2. within each asset class, diversify broadly -> hold value-weighted index (passive) --> if you go active, do so with a clear rationale, diversified approach, and sensitivity to trading costs and active management fees
principle of risky investing
1. learn the easy way! rely on economic analysis and historical evidence, not your own personal experience --> you don't need to build up wisdom by watching the stock market on your own 2. participate! when risk is rewarded, you should always take some, even if you are a cautious person 3. diversify! dividing your investments among different risky assets can reduce risk without reducing average returns 4. don't try to beat the market! individual investors shouldn't try to win by picking stocks: financial markets are efficient and, because of this, very few individual investors can profit from personal trading 5. watch the fees! - fees and trading costs should be kept at a minimum 6. if something looks too good to be true, it is - only fraudulent investments claim to deliver extra return with nno risk whatsoever - there should always be some probability of loss with higher return than you can get with a fraudulent investment
three types of mutual funds
1. open-end funds (most common) 2. closed end funds 3. exchange-traded funds (ETFs)
bond breakdown
1. short-term/intermediate-term/long-term - how often will you get payments for 2. US treasury / corporate / municipal (statee and local gov) - corporate = question of how likley it is the corporation will stay in business long enough to pay 3. investment grade/ high-yield - high yield = ratings agency not sure company will exist long enough to make payments 4. nominal / inflation indexed - from treasury, TIPS = treasury inflation protected securities
Risky asset classes
1. stocks, aka equities - claims to profits of a business, whatever they turn out to be 2. bonds, aka fixed-income securities - promise to make pre-specified payments, won't get more than what is promised 3. real estate, residential or commercial, entitles you to rent on your property 4. commodities (have value in consumption or production, ex. precious metals, crops, crypto)
exception to VW
Dow Jones - price weighted for historical reasons --> by price per share, not market cap --> generally ignored
exchange-traded funds (ETFs)
ETFs are a clever combination of open-end and closed-end features investors can trade ETF shares with each other throughout the day, no minimum purchase amounts BUT only certain institutions can create or redeem shares in the same way a open-end mutual fund would result: keeps the ETF price close to the value of the underlying assets ETF investors only pay capital gains taxes when they sell their ETF shares
General rule with single coin toss
P(H) = p P(T) = 1-p Expectation = p Variance = p(1-p) Standard Deviation = sqrt(p(1-p))
expected return of a risk bond held to maturity
Probability of default: Pdef Loss in default (difference between the promised payoff and whatever creditors can recover in case of default): L Yield to maturity: YTM Expected return = YTM - Pdef*L CONCLUSION: risky bonds may offer higher expected return than safe bonds, but that expected return is not as high as it looks under YTM
real stock return formula
R = D/P + G D=dividend P = current stock price G = growth rate of real dividends D/P = dividend-price ratio aka dividend yield
common VW indexes
S&P 500 - standard and poors 500 large US companies NASDAQ - primarily tech
recent history of bond yield
TIPs first listed late 90s at 4% real ROR during this century, yields on safe bonds have greatly declined
geographical distinction
a geographical distinction can be applied to all of the different assets 1. US 2. foreign developed 3. emerging markets
active vs passive (index) funds
active funds are managed using the judgement of fund managers passive funds simply try to track an index active funds typically charge higher fees to compensate managers, BUT there are some expensive index funds which are ripoffs!
SRI ~ socially responsible investing
active investing to express values --> to avoid investing in (divest from) companies whose business model is inconsistent with your values 1) tobacco companies 2) gun manufacturers 2) private prisons 4) fossil fuel producers **investing with regard to environmental, social, and governance is ESG --> governance = how company we are investing in is governed
hiring an active asset manager?
active mutual funds exist and their managers claim to be able to beat the market - there is evidence some can do this, before fees, although there are also charlatans CONCERN: they charge you a management fee and basic economics suggests that the fee eats up the return
evidence on active asset managers Del Guercio and Reuter 2014
after subtracting the fees, directly sold active funds do about as well as index funds = directly sold active managers earn enough return before fees to cover their higher active expense ratio after subtracting the fees, broker sold active funnds underperform by 1.2% per year = this is close to the extra fees they charge relative to index fees, implying that the broker sold active managers can't beat index funds before fees AND the sales loads make these funds an even worse investment LESSON: YOU SHOULD ONLY BUY DIRECTLY SOLD MUTUAL FUNDS AND, WHILE DIRECTLY SOLD ACTIVE FUNDS WONT HURT YOU, IT WON'T HELP YOU EITHER
real estate breakdown
agricultural commercial residential
commodities
agricultural industrial energy precious metals crypto
is the stock market expensive
alternative awy to look at stock market is to measure stock prices relative to current earnings of corporations b/c of cyclical variation in economy, we use the average earnings over the past 10 years Result: CAPE ratio - cyclically adjusted price-earnings
risk reduction with multiple correlated assets
as number of stocks increases in the limit, by investing an equal amount in each one, you can reduce your portfolio risk to: Var(Rp) = ro*Var(R) Risk of entire portfolio = corr * risk of an individual asset IN REALITY: stocks are positively correlated, such that no matter how broadly you diversify there is still some common risk in the portfolio
default risk of bonds
bond investors consider risk that bond will not make the payment it is promised why? bond issuers may default --> credit rating agencies give bonds letter grades (AAA and below), which higher grades indicating lower probability of default
Bond returns
bonds are fixed future payments simplest: bond promises a single payment (the face value or principle) that is certain to be made [ex. 1 year US treasury bills]
Asset classes
broad categories of assets
taxonomy for asset classes
can be categorized in two dimensions 1. uncertainty of payments 2. time till payments are made (known as maturity of a single payment or duration when we average across multiple payments) risk, measured by std, tends to increase when either payments are more uncertain OR occur in more distant future (greater likelihood you don't get the money)
Normal distirbution
captures the idea of random variables, which reflect the cumulative impact of many small shocks 69% of time, within 1 stdev 95% of time, within 2 stdev 99.7% of time, within 3 stdev
directly sold or no-load fund fees
charge only management fees and operating expenses - investors who know enough to contact mutual fund companies directly should always buy no-load funds
Bayes law
combines two calculations to give: Pr(A | B) = Pr(B|A) * (Pr(A) / Pr(B)) Important: Pr(A|B) ≠ Pr(B|A)
correlated risky assets
considering when the assets move together, because their performance is influence by common factors like performance in the US economy probability of two good/two bad is influence by the factor p, -1<P<1
correlation of bonds and stocks
correlation between assets can change over time = changes potential for risk reduction through diversification for those assets [ex] bonds and stocks late 20th century - positive correlation ~ when Fed raised interest rates to fight inflation (bad for bonds!) it caused recessions (bad for stocks!) ^^^bond-stock diversify bad^^ early 21st century - negative correlation ~ as Fed lowered interest rates (good for bonds!) to fight recessions (global financial crisis, COVID pandemic, bad for stocks!) ^bond-stock diversify good^
correlation
covariance divided by the product of the standard deviations of asset 1 and asset 2 properties: if two assets move perfectly togetheer, corr =1 & covariance=variance if two assets move perfectly opposite each other, corr = -1, cov=-var
management fee
cover the cost of management the money and are paid annually along with other operating expenses
CAPE ratio
cyclically adjusted price earnings ratio stock prices : 10 year average earnings (ex) very high today - buying $1 corporate earnings costs over $35 historical earnings
breakeven inflation rate
difference between the yield of nominal bonds and yield of TIPS bonds reflects the market participants' expectation of inflation (with minor adjustments for risk and liquidity of different bond types) --> if future inflation = breakeven rate, TIPS and nominal treasuries will give the same maturity --> if future inflation higher than breakeven, buy TIPS --> if future inflation lower, buy nominal
comparing stocks to bonds and mmfs
even though stocks are expensive today and R is likely low: bonds and money market funds have extremely low yields today = expected return on stocks is still attractively higher than return on mmf and the yield to maturity on bonds --> approx. 5% higher
iron law of active investing
every dollar of active outperformance by someone is accompanied by a dollar of active underperformance by someone else, b/c the passive investor earns the average return and not everyone can be better than the average SO: active investing should only be done if you have a convincing theory of how you will win and who will lose
Variance
expectation of the squared deviation of winning from its mean Var[X] = Pr(A).* (A-mean)^2 + Pr(B)* (B-mean)^2
extremely bad past performance is important to note
extremely bad past performance is predictive of bad future returns after fees the worst performing funds lose almost all their investors and raise fees on the remaining (inattentive) investors to cover their fixed costs of staying in business
Distributions in finance
fatter tails! reflects the occurrence of occasional large shocks as opposed to the accumulation of small shocks normal randomness is a standard combination of smaller bits of news, BUT large, huge global shocks are possible every once in a while
12b-1
feed paid annually and cover the cost of providing information to investors
closed-end fund
fund issues shares when it is created and then investors trade these shares with each other fund is traded like a stock, throughout the day, with no minimum purchase amount price is whatever investors are willing to pay for the shares --> this can differ from the value of the underlying assets, depending on whether investors are optimistic or pessimistic about the skill of the fund manager in relation to the fees the manager charges the fund --> often the closed-end funds initially trade at a premium to the underlying assets, then later on at a discount
don't bother to chase performance
given that money flows kill performance, chasing good past performance is pointless
value-weighted index
holds the companies in proportion to the total dollars invested in that class ex. if it was just a class of Tesla and Apple and Tesla had 75% of money invested in that class and apple had 25% --> these are the weights for how much stock would be held of each
market beta
how much that stock is expected to move when the market moves beta 0.8 means that stock will rise 0.8% when market rises by 1.0%
bond price and return relationship - the yield or yield to maturity
if bond is held to maturity: the lower the price, the higher the return or yield --> steeper slope win the graph of time to log value further away maturity date means change in slope (yield) as a result of changing interest rates has a larger effect on the bond price --> this is why long-term bonds are risky to short-term investors: if you don't hold the bond to maturity, you could lose money due to price changes in relation to income
risk reduction with two correlated assets
if corr = 1, diversificationn does not reduce the variance of the portfolio return at all <-- worst case for diversification if corr=-1, the varaince of the diversified portfolio is 0 <-- best case for diversification if they are not perfectly correlated, there is always some benefit from diversification
factor p for correlated risk assets
if p is positive, increases the probability of two good, two bad --> moving together! if p is negative, decreases probability of two good, two bad --> assets are moving against each other
danger of extrapolation
if you look at capital gains, bonds look great period of declining bond yields (interest rates) has delivered very high bond returns (rises in price) -> as yields have fallen, bondholders have enjoyed capital gains but, this can't continue because eventually the bond yields would have to become negative, an unreasonable expectation CONCLUSION: recent return experience is not a guide for the future --> in fact, higher recent returns now imply lower returns in the future
stock returns
if you own a stock, you are a part-owner of a corporation result: - you have right to vote in certain corporate decisions - you receive dividends, the portion of corporate profits (earnings) that is paid out to shareholders rather than being reinvested to grow the business difficulty: no single promised payment = we analyze stocks using current dividends and making an assumption about the growth of the business
passive investing
investing in vehicle that tracks a market-weighted index or portfolio --> if you hold VW index for an asset class, you earn the same return as the average dollar invested in that asset class --> called passive because: once you buy the VW index, minimal trading is needed to maintain the position - price changes adjust the weights automatically, so you only need to trade when companies issue new shares, companies join the asset class or drop out --> by holding the VW index, you guarantee yourself average performance and protect yourself from doing worse
black swan
large shocks that have never been seen before --> BEWARE the fat tails have major implications for risk management --> anyone taking financial risk should consider both the standard risks captured by the normal distributions as well as the possibility of fat tail events, i.e. the black swans completely outside of past experience
Explointing base rate neglect
make your company look like recent successes, use stereotypes of success Manipulate the thinking that Pr(Great investment | lose money to grow) = Pr(losinng money to grow | great investment) , ignoring pr(great investment is so low
familiarity vs safety
many ppl feel they can pick stocks without taking risk b/c they think certain companies are safe investments, but this is a common misconception any company/sector/country can have unexpected bad news --> NEVER invest in stock of your employer substantially because your salary depends on that company too ex. the Enron case where workers invested their retirement savings to reduce risk, diversify, don't depend on familiarity
Base rate neglect in finance
may lead investors to react to much to recent returns of mutual fund managers, thingking Pr(Skilled manager | high recent returns) = Pr(High recent returns | skilled manager) people here are forgetting that there is a very low base rate of Pr(Skilled manager)
risk
measured as standard deviation of the return
why does investment horizon matter to measures of risk aversion?
more aggressive strategies are for people with a longer time horizon 1) the probability of losing money in risky investments declines with the time horizon - b/c people dislike loss, longer time horizon makes it easier to tolerate risk 2) long-term bonds are safer for people who can hold them to maturity and ignore the impact of yield changes - similar for stock price changes
mutual fund fees
mutual fund managers can charge a variety of fees to their investors: front end load back end load management fees 12b-1
key figure from Barber and Odean
net return = gross return - trading costs gross return = flat! after subtracting trading costs <-- the active traders get lower amounts = make less after the removal of the costs!!!!
principal of participation
no matter how averse you are, you should always invest something in risky assets (as long as there is a return on the risk) * you should always participate in risky asset markets --> once you have 3-6 months income in the emergency fund
Nominal vs. Inflation-Indexed bonds
nominal treasury bonds make safe payments in current dollars (rate = nominal interest rate) treasury inflation protected securities (TIPS) make safe payments in real dollars (rate = real interest rate)
return
on a risky investment over one period, defined as the money you get back next period if you sell, less the price (cost) of the investment today when you bought it, divided by price today money from next period include both income (a coupon for bond, dividend for stock, rent for house) and the price at which you can sell it next period the increase in price on an asset (capital gain) is only taxable when you actually sell the investment
hedge
one asset is a hedge for another when they move perfectly opposite one another with a correlation = -1
back-end load
paid upon sale, depending how long the shares have been held
Base rate uncertainty
people can disagree about the base rate --> in this case, the base rate (unconditional probability) is known as the prior and the conditional probability givenn by Bayes' law is a posterir --> different people can thus have different priors and therefore different posteriors --> ex. COVID, people have different priors w.r.t. the base rate of getting sick = led to different interpretations of test probabilities
active investing
picking a portfolio with the intention of outperforming the VW index
conditional probability
probability of one event given the other Pr(A | B) = Pr(A,B) / Pr(B)
unconditional probability
probability of one event without knowing the other Pr(A), Pr(B)
joint probability
probability of two events occurring together Pr(A,B)
covariance
probability weighted average of the product of the demeaned returns for asset 1 and asset 2
Expectation aka Mean
probability weighted average of your potential winnings E[X] = Pr(A)*A + Pr(B)*B
why avoid risk?
pure risk without reward = unappealing most people feel that the utility of an extra dollar is lower the more dollars you already have --> so, you turn down risk because the value of the dollar you might win is less than the value of the dollar you already have
understanding risk
quantitative measures of risk can be helpful, particularly: 1) the standard deviation of your portfolio return 2) the BETA of your return, defined as the regression coefficient of your return on the market return --> if the market goes down by 10%, you should expect your portfolio to go down by (10*beta)% --> beta<1 means portfolio safer than the market, beta>1 riskier than the market BUT these quantitative measures do not capture the impact of extreme events like black swans
Standard deviation
removes the concern of having units that are squared Std[X] = Sqrt(Var[X])
stock risk
rewrite R = D/P + G price P = D/ (R-G) can change for following reasons: 1. dividends change (but this is not very volatile) 2. expected future growth changes 3. expected return changes (perhaps because interest rate changes or the interest premium investors demand changes) So, large changes in R and G can have large effects on price --> especially when R-G is already very small so we are close to dividing by zero --> --> when future expected return goes down (R), denom gets smaller and price goes up SO you should not extrapolate past returns to forecast future returns
low-risk investing
risk of stock can be emasured by its volatility (standard deviation of return) or the market beta --> in practice, low volatility stocks also tend to have low market betas there is long-term historical evidence that low-risk stocks have almost as high an average return as high risk stocks, so you can: 1. lower risk without reducing return by holding the same dollar value of low-risk stocks OR 2. increase return without increasing risk by investing more dollar in low-risk stocks WHY DOES THIS WORK? WHO IS LOSING? some aggressive investors who can't borrow to buy stocks drive up the price of high risk stocks so that these stocks offer too low a return in relation to the risk --> as a less aggressive investor who would otherwise hold cash, you can do better by reducing your cash holding and investing in low risk stocks CAVEAT - low risk investing does not always beat passive investing - low risk stocks did particularly bad in 2020 because they are often physical businesses like utilities that really got hurt during the pandemic
why is risky valuable
risky asset classes generally offer higher average returns than safer asset classes AND higher average returns are extremely valuable, esp. if you are investing over a longer period of time BUT this higher average return may not be realized = RISK
risk and return
risky asset classes offer higher returns than safer asset classes
front-end load
sales charge (commission) paid upon purchase to compensate brokers for their sales efforts
small-cap investing
small cap stocks have low market capitalization (low total dollar value of their shares) long-term historical evidence that these stocks deliver high returns relative to their risk caveat = do not always beat large-cap, i.e. late 1990s, late 2010
least bad active strategies
some active strategies have both theory and long term historical evidence to support them 1. low-risk stocsk 2. value stocks 3. small-cap stocks **all these strategies are consistent with broad diversification and can be implemented cheaply --> don't need to pay massive management ffees to take these approaches HOWEVER! we don't know if thesis will continue to work :0
how much risk to take
stanndard rule for portfolio choice is that the share of your wealth you should invest in a risky asset is [(portfolio mean return) - riskless interest rate] / (risk aversion)^variance
bear market
stock market down (bear swipes paw down to kill you)
bull market
stock market up (bull brings horns up to kill you)
stock picking and skill
suppose you do have the skill to systematically beat the market --> the most profitable way to use this skill is to invest professionally as a mutual fund manager, hedge fund manager, etc. SO we should expect skilled individual investors to be extremely rare because the rewards to skilled professional investing are so high
trading costs
technology has lowered trading costs and brokers no longer charge commissions after the emergence of Robinhood BUT you still pay a higher price when you buy than you get when you sell it by at east $0.01 (MINIMUM PRICE INCREMENT) -->market AND if you trade large amounts, you have price impact - i.e. you move the price against you!
stockpicking
the worst active strategy - many individual investors are tempted to be on individual stocks but there are serious problems with this approach 1)special information you think you have about a company is probably already reflect in the stock price because other people i have that information and they are also placing their bets (the crux of the efficient market hypothesis) 2) if you do have information that is not in the price, it may be illegal to trade (insider trading) 3) trading costs reduce your profits 4) betting on individual stocks reduces the risk-reduction benefits of diversifying through many stocks
risk aversion
to measure, we look at how fast marginal utility declines: -- utility is inversely proportional to the power of consumption U'(C) = 1 / C^gamma --gamma is the coefficient of risk aversion (ex) if gamma =2, doubling consumption cuts the marginal value of an extra dollar by a factor of 2^2 = 4
Base rate neglect error
to neglect the ratio of Pr(A) / Pr(B) the unconditional probability of Pr(A) is known as the base rate, thus we have base rate neglect
market capitalization (cap)
total value of all a company's shares
insider trading
trading on inside information is illegal whenever that information belongs to someone else 1) an employee trading on knowledge of a company's business results or strategy is stealing info from the compnay 2) a friend or family member who learns the information from a compnay employee is profiting from stolen information SEC regulates heavily post 1930 scandals with the crash, regularly prosecutes and wins
Considering past returns?
two problems with considering past returns: 1. performance is largely driven by luck over the short period (1-3 years) a. too much noise b. doesn't reflect skill for outperformance 2. over longer periods (5-10 years), luck averages out so past performance does reflect skill - but these skilled managers still do not deliver return to investors going forward AFTER FEES --> Why? money flows kill performance i. once investors see consistent performance in a fund, they put money in ii. this makes it harder for the managers to deliver results iii. with a bigger fund, they move prices against the fund when they trade (the fund has price power) = they may still earn the same dollars from their trades, but now the percentage return is lower iv. money keeps flowing in until performance deteriorates to the point where it just equals the fees the managers charge SO skilled managers end up running larger funds = higher dollar fees but performance that just covers the fees = leaves nothing left for investors
diversification
used for risk reduction of a portfolio - varying the set of assets you are invested in in order to reduce the overall risk of your portfolio
value investing
value stocks have low market prices relative to accounting measure of company's fundamental value such as earnings or book value growth stocks have high market prices relative to accounting measure of fundamental value --> there is long-term historical evidence that value stocks beat growth stocks and have somewhat lower risk (warren buffet does this) --> simplest theory explanation = hgih market prices relfect both future prospects of company and irrational enthusiasm of some investors for that company --> so many growth stocks are overpriced and you should underweight them CAVEAT: value stocks do not always beat growth stocks (disastrous in 2020 and 2010-2020 due to nature of pandemic --> value companies hurt while growth companies were insulated)
open-end funds
you can buy or sell shares from the mutual fund. company at the end of each day --> there is usually a minimum purchase amount price of share is the fund's net asset value (NAV), which is computed from the closing price of all the assets owned by the fund it is up to sales managers to keep enough cash on hand to pay off shareholders who want to sell the fund owes capital gains taxes on shares and they pass this on through to all share holders whether they sell their mutual fund shares or not
Key SRI points
you should expect SRI to lower your average return --> be suspicious of "beat the market and do good" --> point of divestment is to drive down the prices. of bad companies, raising their cost of capital and driving them out of business = RESULT--> implies that bad stocks will deliver higher returns because you have driven down their prices relative to good stocks, so the ones who invested in bad companies will earn more return CAN STILL BE MODEST if you continue to diversify. your portfolio!
