Fundamentals of Investments

What factors effect IR and make money today worth more than money tomorrow, and how?

Impatience: rather consume now than later 1→1+r

Risk: risk to not receive or receive less-than-full basket (risk premium)

Inflation: Price levels tendency to change

Define and give formula for annuity

Fixed CFs at specified frequency over fixed time period

Define and give the formula for perpetuity and growing perpetuity

infinite series of periodic CF

growing at constant rate

What is the formula for an infinitely lived stream of CF, NPV of constantly growing CF and value in terms of T years money

Formula for risky cash flows

Define investing

the process of committing resources today for the acquisition of an asset that is expected to generate some benefits in the future

What categories can assets be divided into and what do they do

Real: land, knowledge, machinery (generate net income in the economy)

Financial: contracts on who gets share income generated and control of assets (facilitate accumulation of income-generating assets, distribution of income from real assets)

Debt/fixed income securities

form of securitized borrowing

lender receives debt security it can hold to maturity of sell to another investor

borrower receives money, pays back in coupon and then par value at maturity

What are the market segments for fixed income securities

Money market: one or less years to maturity (government bills, bank certificate of deposit, firm commercial paper)

Bonds: 1< year to maturity, 1<t<10=notes

What are the sources of risk in fixed-income securities? (2)

IR risk: +IR, - value of fixed security (longer maturity larger risk)

Credit risk: inability to pay coupon or par value (govn small, corporate varies vastly)

What are the rights that come with equity securities:

Control: right to appoint board of directors, vote on issue brought to general meeting

CF: right to firms profit, payed as dividends

Define indexes, (give example eq)

Basket of securities chosen following a predetermined rule, ex global, style, local

Define financial markets

where buyers and sellers of financial securities meet to exchange securities and cash under predetermined rules

What is the financial market’s role in a well-functioning economy (6)?

1. trade facilitation (transaction and price)

2. price signalling

3. allocation of resources

4. timing of consumption

5. sharing of risk (diversify away)

6. separation of ownership and control

What are the implications of a well functioning financial market?

highly competitive - high reward possibility

→lots of talent and resources →unlikely to find free lunches/all relevant info reflected in prices → expected profit depends on risk not informational advantage

What are the two financial sub-markets

primary: initially created and sold, capital raised from investors

secondary: investors trade among themselves, money moves between them, indirect benefit to issues as it facilitates well functioning primary market

What are the four different market types?

direct, brokered (primary), dealer(secondary), auction

Describe the auction mechanism

order book consists of ask (sell) orders and bid (buy) orders. Market orders (buy lowest p, sell highest p) get matches with existing limit (specific p) orders in order book. Limit orders put into order book until market order matches

define bid-ask spread what is the effect costs?

difference between lowest ask price and highest bid price

wider spread, higher implicit cost of trading

commission: fee payed to broker for facilitating trade

What is buying on the margin

the agreement where an investor borrows part of the total purchase price of a security, pays the broker back the borrowed amount + interest

What is short selling?

Refers to selling a financial security the investor does not own.

investor thinks the stock will decline, borrows from a broker, sells the stock, buys back later and returns to lender → if the prediction is correct profit earned

What are the two main decisions when it comes to portfolio allocation?

Asset allocation: how much to invest in each asset class

Security selection: which particular assets to hold

What are the two approaches to portfolio construction?

Top-down approach: asset allocation into broad asset classes, then security selection (more common and advised)

Bottom-up approach: security selection (chooses best securities), asset allocation is simply an effect of security selection

What is the law of one price?

Two assets that have the same future CF should have the same price today

What is arbitrage and why cannot it not occur?

If two assets have the same future CF one is cheaper, an investor can buy the cheaper asset and short it for the more expensive one, earning the difference as profit today. In the future positions offset and net CF =0

Law of one price holds and arbitrage opportunities not available

What are the formulas for return for one period? and what are the sections called

Second equation: 1st part capital gain rate, 2nd part dividend yield (>=0 because either 0 dividends paid or pos)

What is the formula for return of multiple periods?

Define expected return

expected value if future return, if held for infinite period of time average return = Er

Define risk, volatility, and what does it imply?

Uncertainty related to future earnings, the standard deviation of returns → volatility, high volatility/SD mean potential future returns are dispersed widely around the expected return

What is the formula for T-period volatility?

one-period volatility * sqrt T

What is the formula for asset price?

What is the efficient market hypothesis?

That asset prices reflect all relevant information instantaneously (immediate price reaction)

When positive news arrives, investors rush to buy the asset pushing the price up until the price in the market equals fair value under new information (and vice versa for negative)

If markets are efficient investors cannot earn higher returns by gathering and processing information and trying to identify undervalued assets

What are the three versions of the efficient market hypothesis?

Weak: asset prices reflect all information that can be derived from past trading data

Semi-strong: prices reflect all publicly available information

Strong prices reflect all relevant information

Describe what this figure depicts, dotted vertical = arrival of new information, why is it not relevant to the real world

Underreaction: price moves immediately in the right direction but not enough

Overreaction: price overshoots and moves by too much

These are cases of inefficient initial price reaction, followed by drift towards the far value over time

It is not relevant as prices jump continuously and seem random due to the arrival of new information constantly

What are the implications of efficient market hypothesis for investors?

There is no point in active portfolio management, no assets are undervalued, if an investor believes an asset is undervalued, it means the investor’s assessment is too optimistic (too high expectations of CF or too low discount rate)

expected return is only dependent on riskiness and not informational advantages

What are some reasons investors are not rational? (7)

memory bias (too much weight on recent evidence)

overconfidence (overestimate precision of their own belief)

conservatism (too slow to update their beliefs)

sample size neglect treat small samples too representative of entire population)

framing (react differently based on how information is presented)

mental accounting (segregate financial decisions into various categories)

regret avoidance (make decisions to avoid regret=

What is the formula for the expected return of a portfolio using weights of returns?

U = expected return

What is the formula for risk of a portfolio?

sqrt:

Define diversification

Reducing portfolio risk by investing in less-than-perfectly correlated assets (pab < 1)

How does this figure show the benefits of diversification?, and how does correlation change between the different lines from left to right

A and B are less-than-perfectly correlated, meaning an investor investing all her into an asset A can increase her expected return and lower the risk by investing some in B, moving along the line from point A to point B

leftmost: perfectly negatively correlated, correlation increases from left to right, rightmost: perfectly positively correlated

What is covariance and the formula for it?

A measurement of the complement between asset returns

To estimate the variance of N assets, how many variances and correlations of you need

What is the efficient frontier, global minimum variance portfolio, inefficient portfolios, what is the efficient frontier for 3 and assets

Efficient frontier: the line that represents the efficient frontier that has the highest expected return for the given level of risk

Global minimum variance portfolio: the portfolio with the lowest possible risk (leftmost tip)

Inefficient portfolio: Portfolios in the inner region of the efficient frontier, exist portfolios at the same given level of risk with higher expected asset returns

Adding more assets shifts the efficient frontier to the left, solid line 5, dashed line 3 (depicts the benefit of diversification)

What is the reason for improvement in diversification?

It is due the the less-than-perfect correlation between the returns of the assets

Can you diversify away all risk?

dashed: pab=0 (diversification possible, adding more assets lowers risk until it becomes basically riskless)

dotted: pab=1 (diversification has no effect)

solid: volatility =0.5, pab=0.5 (As N approaches infinity the marginal effect of increasing N decreases and eventually plateaus)

When pab>0 then the variance of an infinitely well-diversified portfolio will also be positive, not all risk can be eliminated and even in infinitely diversified portfolios some risk will remain

Define utility and what is its formula

A single value mapping the two dimensions of a portfolio, expected return and volatility (risk), it is a way to measure an investors degree of happiness with a portfolio

A=investor’s coefficient of risk aversion

What does it mean if risk aversion is: A>0, A=0, A<0

A>0; risk-averse; dislikes risk, willing to trade off some expected return to reduce risk

A=0; risk-neutral; investor does not care about the risk of the portfolio, only expected return

A<0; risk-loving; investor prefers portfolio to have more risk than less

At which points is the investor indifferent and which give more and less utility?

Indifferent: portfolios Q,P,R

More utility: portfolio T

Less utility: portfolio S

What is the slope of the indifference curve?

Slope=investors risk aversion

Steeper: higher risk aversion coefficient, risk-averse, prefer little risk

Flatter: lower risk aversion coefficient, risk-loving, prefers more risk

What is investing in a positive and negative amount in a risk-free asset equivalent to?

Negative amount (shorting): borrowing from the bank

Positive amount: depositing amount in a bank

What is the equation for expected return of portfolio, a portfolio of one risky-asset and risk-free?

w=sigmac/sigmap, rearranged from sigmac=w*sigmap

w(up-rf) = (sigmac/sigmap)*(up-rf)

Define risk premium

The difference between the expected return of a risky asset and a risk-free rate of return, and is a measure of how much more expected return the risky asset offers in compensation for the risk-free alternative

What is the formula for volatility of a portfolio with one risky and one risk-free asset?

What can you say about the linearity of two assets?

rf and risky asset: linear relation between the expected return of a portfolio and its volatility

two risky assets: typically non-linear but dependent on the correlation of their returns

What is the capital allocation line and what does it mean if the investor is at rf, p, in between or to the left of p on the graph?

At rf investor is investing all of their wealth in rf (w=0)

At P investor is investing all of their wealth in risky asset p (w=1)

In between, investor invest part in rf and part in P (0<w<1)

To the left of P, investor is borrowing money and investing in risky asset P (w>1)

What does the slope of the capital allocation line measure and what is its formula?

It is a measure of the risk-adjusted expected return on the risky asset P, ratio of the risk premium and volatility of P: Sharpe ratio

How does an investor chose a portfolio along the capital allocation line?

Choose the portfolio with the highest possible utility; the point where the highest possible indifference curve touches the capital allocation line. Any other point has a low utility than C*

How do you find the optimal portfolio of consumption analytically?

expected return and volatility into the utility function

derive U with respect to w and set equal to 0

solve for w*

What are the steps to portfolio optimization with many risky assets?

1. solve for the optimal portfolio of risky assets only, tangency portfolio: the highest possible portfolio expected return for any level of volatility given by capital allocation line with the highest possible slope (highest Sharpe ratio) that tangents the efficient frontier

2. solve for optimal allocation between rf and tangency portfolio (derive utility function, make equal to 0, solve for w*)

What is the formula for asset price?

u=expected return of the asset

How does an investor's decision to buy an asset effect expected return?

An increase in demand must be matched by a decrease in price so because of the pricing identity, an investor’s decision to buy an asset results in it having a lower expected return

Define idiosyncratic and systematic risk

idiosyncratic: diversifiable asset-specific risk, Investors do not need to be compensated for

systematic risk:: non-diversifiable, variation in returns common to all assets, investors need to be compensated for (risk premium)

What are the main assumptions of CAPM (4)?

1. all investors are price-takers, buy and sell at market prices, lend/borrow at rf, no frictions (perfect competition)

2. two kinds of assets (risk-free and risky)

3. all investors hold efficient portfolios, the highest yield expected return for a given level of volatility

4. all investors have identical al expectations regarding expected returns, volatility and correlations

What are the components of an investor’s portfolio and how do they differ?

Market portfolio (rf asset and tangency portfolio) and risky asset

investors hold the same amount of risk free asset and same amount of risky portfolio

What is the formula for risk premium in CAPM?

Systematic risk = Beta

compensation for bearing one unit of risk um-rf, market risk premium

What is the formula for systematic risk?

element of real numbers

What is the formula for reward-to-risk ratio for asset i?

Why in equilibrium is reward-to-risk ratio the same for all assets?

Price identity, if an asset offers a higher ration, investors would rush to buy it pushing price up and pushing expected return down

What is the reward-to-risk formula for the market portfolio?

What does it mean for the price of an asset if the beta is 0,1, >1, 0-1, <0?

B=0; no systematic risk, investors willing to pay a high price, low ui required = rf

B=1; As risky as the market portfolio, risk premium=market risk premium

B>1; ui positively correlated to um, and volatility is higher, contributing a lot to riskiness, low price, and high risk premium for holding the asset

0<B<1; positive correlation with market portfolio but lower systematic risk, lower risk premium

B<0; ui negatively correlated with um, decreases overall risk of investors portfolios (insurance-like feature), high price, very low ui accepted, negative risk premium

What is the formula for excess return and beta from regression?

Rt= rf-rt

What is the formula for price of risk and why can it be used?

It can be used as increasing beta by one is the same as increasing expected return by market risk premium

What is a factor model and what are the components?

A model that posits an assets realized return over the risk-free rate:

time-invariant constant return(alpha), return due to exposure to systematic factor(beta, RM,t), idiosyncratic return (ei,t)

What is the formula for the single-index model ?

systematic factor = return of market index

How does the single-index model capture facts of returns?

all assets have the same beta exposure to the same market index return, so asset returns on average are positively correlated (high beta, comove more strongly with the market index)

Idiosyncratic risk (e), is uncorrelated, resulting in less-than-perfect correlations between assets

time-invariant (alpha), non-zero average excess return not due to beta exposure to market return

What is the single-index model risk premium formula?

What is the variance of asset return from the single-index model?

What is the formula for alpha, beta and idiosyncratic return in the single-index model?

What is the formula for idiosyncratic variance in the single -index model?

What are the steps to test CAPM?

1. collect historical returns of N test assets, market portfolios, and rf asset

2. estimate beta for each test asset (regression), N beta estimates produced

3. calculate the average average excess return for each test asset , N average returns produced

4. estimate parameters, relating excess returns to betas through regression ( beta independent, average excess return dependent)

What does the CAPM imply about the values of the coefficients y0 and y1?

y0=0, y1=average excess return of market portfolio

What have researchers found about the true values of yo and y1, and what does it imply?

y0 significantly >0

y1<average excess um

Investors do not get as much extra risk premium for holding a higher beta asset as CAPM implies, the security market line is much flatter, suggesting CAPM is not the true asset pricing model

What is the security market line?

A graph depicting risk premium as a function of beta

Why does CAPM fail? (2)

1. strict and unrealistic assumptions

2. true market portfolio is not observable as it contains non-tradable assets like human capital

What is size effect and what causes it?

Small firms tend to have higher stock returns than larger firms

Risk; small firms might be riskier than larger firms, and investors require higher ui or systematic

Mispricing; underestimating the value of small firms, overtime this corrects and the realized returns of small stocks are higher than those of large

Define valuation ratio

market-based valuation of a firm’s equity (stock price, mark cap) relative to accounting-based valuation (book value of equity, EPS)

What is value effect and what causes it?

The tendency of stocks with low valuation ratios (value stocks) to have a higher return than high valuation stocks (glamour/growth stocks)

Market price cheap compared to book value, historically higher returns than market price high relative to book value

Risk; Value stocks are riskier than glamour stocks

Mispricing; underprice value stocks, overprice glamour stocks

What is value investing?

Investing in value stocks (market price relatively low compared to book value), and shorting/avoiding glamour stocks (market price high compared to book value)

What is the momentum effect and what causes it?

The tendency of stocks with higher past returns (winner stocks) to have higher future returns than stocks with low past returns (loser stocks)

Risk; momentum crashes, long-term average returns to buying winner, shorting loser are largely positive, rends rot suffer infrequent large loses

Mispricing; underreact to new information, stock prices drift slowly towards efficient value

What is momentum strategy?

Buy-ing winner stocks (book value>market value) , shorting loser stocks (market value > book value)

What is the three-factor model by Fama and French and what is its formula?

Breaks down excess return into three components, time invariance alpha, idiosyncratic return and return due to systematic factors; value (high minus low, high book-to-market ratio - low book-to-market ratio), size (small minus big), momentum

Define bond and the keywords associated with it

Bond. borrowing arrangement in the form of security, the most common type of income security, used by firms and the government to finance projects and operations. All payments, size and timing are fixed when bond is issued

The issuer pays the par value of the bond at maturity and period coupons (coupon rate * par value)

What is the bond pricing equation?

F = par value

c= coupon rate

Inverse relation between bond price and interest rate

What is YTM maturity of a bond?

It is the interest rate r, which makes the theoretical price equal to the market price

What is a credit rating, and what is its effect on pricing?

The amount of credit risk (risk of the issuer not having sufficient resources to pay payments) an issuer or a bind carries

The higher the credit risk the higher the r investor will apply to discounting future CF from the bond, lower price

What is term structure of interest rates?

It is the fact that yields (yt, annualized interest rates used to discount CF occurring t years in the future)vary across maturities

What is the formula for bond pricing taking into account term structure?

What is a zero-coupon bond and what is the formula for price and yield from it?

A zero coupon bond is a bond that does not pay coupons, only par value at maturity

What is the formula for PV of coupon payment using formula for yt from zero-coupon bond?