FINC13-303 Study Guide - Midterm Guide: S&P 500 Index, Risk-Free Interest Rate, Sharpe Ratio
TYPES OF MARKETS
Direct Search: Buyers and sellers seek each other out directly [Gumtree]
Brokered: 3rd party assistance in locating buyer or seller [Real-Estate]
Dealer: 3rd Party acts as intermediate buyer/seller [Primary market]
Auction: Direct transactions among public orders [NYSE]
Effective Costs of Trading: Bid-Ask Spread, Brokerage Fees, Transaction Costs,
Commissions, Taxes, prices @ multiple levels
Bid-Ask Spread: Bid: What the broker is willing to buy at, Ask: broker sell at
TYPES OF ORDERS
Market order: buy/sell orders to be executed immediately at the best price
Limit buy order: order specifying price investor is willing to buy a security.
E.g. buy a certain number of shares when the price goes below X
Limit sell order: order specifying price investor is willing to sell a
security. E.g. sell a certain number of shares when the price rises above X.
Stop loss order: the stock is to be sold if its price falls below a certain level to
stop further losses
Stop buy orders: stock should be bought if it rises above a certain limit (e.g.
during short sales you want to limit potential losses from short position.
BUYING ON MARGIN
Securities purchased with money borrowed in part from the broker. Investor
magnifies upside and downside risk. Increases net worth of account.
Margin: portion of the purchase price contributed by the investor
Maintenance margin: If margin falls below this level, broker issues a margin
call and investor must top up account. Account closed and funds liquidated to
pay loan if investor doesn’t act. Can fall to
Return:
SHORT SELLING
Sale of shares not owned by investor but borrowed from broker and later
purchased to replace loan. Margin account = proceeds from sale + 50%
margin. Dividends paid to lender. Purpose to profit from a price fall. Price can
rise to
Profit = decline in share price x # of shares sold out
Makes markets efficient as lots of people searching for information
How far can price fall?
Short Selling Stocks (want price fall)
-sell and deposit proceeds + margins in account
-close out position by buying back
-
75 = 1.3P
FORMULAS: Returns, Variance, SD
Discrete Periods Returns (HPR): forecasting based on a past sample. Note:
dividends assumed to be paid at end of period.
T periods: single period
Continuous compounding returns (CCR):
T periods: single period:
Aggregating:
Arithmetic Av: ignores compounding. Doesn’t represent single equivalent
rate. Good if only have historical performance. Used to forecast.
Geometric Av: time weighted. Single per period return to give same
cumulative performance as overall return. artificially inflated returns.
IRR: dollar weighted. Discount rate equating future CF to initial investment.
APR: annualises period returns ignores compounding.
EAR: rate at which funds grow. As n grows EAR & APR grow further apart
Expected Return: mean value of distribution of HPR (reward from
investment). Average return fluctuates most over time
Variance: expected value of squared deviation from the mean.
probability weighted
of a sample
or
SCL/SIM
is the systematic risk and is the unsystematic (residual) risk
SCL/SIM
SD: best measure of risk. Measures in same dimension as E(r).
p = portfolio of risky and rf.: risky asset. RF Var=0
Proportionality: Given:
Inflation:
Theory: Higher risk demand higher risk premium. Assuming risk-free
unaffected increase in risk premium = increase in
TVM: 1. Preservation of purchasing power 2. Compensation for deferral of
consumption 3. Incentive to take on risk
PORTFOLIOS
Risk premium: reward. Return excess of rf rate.
Covariance: measures tendency of two assets returns to vary in tandem.
There are n*(n-1) covariances in a portfolio
Sample
Given probabilities given correlation
SCL/SIM (COV OF i and J)
Correlation: -1< <1. Asset contribution to portfolio depends on with other
assets & own Variance. Benefit as long as is < 1
Efficient Diversification: Diversification depends on covariance; smaller
correlation leads to greater benefit; benefit exists when Cor(ra,rb) < 1
Optimal risky portfolio (bond)
Weights eg:
Minimum Variance weights
CAPITAL ALLOCATION
Reward-to-Variability (Sharpe): use nominal figures (ave.
returns no inflation). grows at
CAL: risk-return combinations achievable by varying
allocation between RF and ORP. Points beyond P possible
by borrowing at RF. Slope of CAL = Sharpe ratio. Sharpe
ratio constant for all portfolios on CAL.Want to maximize.
Risk Aversion: reluctance of investor to accept risk. All assumed risk averse
but differing levels of tolerance. Can be measured as price of risk demand
(risk required to compensate for taking on 1 unit of risk
Utility: Risk Neutral: Highest not U as A=0
optimal CAL (y) can be found by dividing risk premium by risk aversion.
Portfolio weights of C* are given by and OCAL
Markowitz: determine set of efficient portfolios by maximising E(r)
for given level of risk. This gives Efficient frontier: graph of set of portfolios
that are mean-var efficient. Starts at MVP which is the portfolio with smallest
variance
ORP: best combo of risky assets to mix with to form complete portfolio. Point
where Sharpe ratio is maximised (slope) – tangent to efficient frontier
CML: CAL that results from using a passive strategy that treats a market index
portfolio (S&P 500) as the risky asset. Tangent to efficient frontier
Separation Property: 1. Determination of ORP and CAL (technical) 2. Personal
choice of best mix of risky portfolio & asset
to maximize utility
Theory: Passive investing: avoids security
analysis and costs associated with it. Based on
notion that securities are fairly-priced. Portfolio mirrors the corporate sector
of broad economy
Costs/benefits of passive investing: 1. Inexpensive and simple 2. Expense
ratio of active mutual fund averages 1% 3. Expense ratio of hedge fund
averages 1-2% +10% returns above rf 4. Active management offers potential
for higher returns
Systematic risk: (market) risk factors common to whole economy. Measured
by the beta (slope of CML)
Unsystematic risk: (firm specific/idiosyncratic) risk that can be eliminated by
diversification. Reduce unstst-risk (and SD) by combining assets where <1
If ratio of systematic to total var increases correlation will increase as well
Asset Allocation: Portfolio choice among broad investments classes
Complete Portfolio: Entire Portfolio, including risky and risk free
Capital Allocation: Choice between risky and risk free assets
CAPM ASSUMPTIONS
CAPM: Model that relates the required rate of return on a security to
systematic risk . It is a equilibrium model. When the CAPM relationship is
violated (e.g. αi is not equal to 0), all investors adjust their holdings (of stock
i) to restore the equilibrium relationship
1.Markets are perfectly competitive & equally profitable to all investors – a.
No investor’s wealth affects market prices b. All info is publicly available at no
cost c. all securities publicly owned & traded thus all risky assets in
investment universe d. No taxes on investment returns (all investors realize
same returns) e. No transaction costs that inhibit trading for investor’s f.
lending & borrowing at common rf rate unlimited
2. Investors are alike except for initial wealth & risk aversion; so all choose
investment portfolios in the same manner - a. investors plan for same time
horizon b. investors rational mean-variance optimisers c. investors are
efficient users of analytical methods & under homogenous expectations use
same inputs & consider same portfolio opportunity sets.
Implications: ORP for all investors is a combination of rf asset & MP
*No other risky portfolio is better than the MP (over time) At ORP Sharpe is
maximised
Problems testing: 1. The
theoretical market portfolio is
unobservable, therefore cannot
be (directly) tested. 2. We can
only observe actual returns, not
expected returns 3. Time-varying
betas
SML: fairly priced assets should plot along the SML. Overpriced plot under,
under priced plot over. if CAPM ER>asset ER asset has negative alpha
Beta: portfolio beta is weighted average of individual securities
Beta = Little number – big number (Given 2 returns)
= =
Differences between the CML and SML
CML SML
The CML is a specific capital allocation line.
It is the capital allocation line formed with
the risk free rate and the market portfolio
The CML is the relation between E(rm) and
total risk (standard deviation)
The SML is the relation between E(rm) and
the systematic risk measure beta
The CML consists of the set of portfolios
formed by combining the market portfolio
The SML is the set of all assets
SINGLE INDEX MODEL (SCL)
SCL: formed by single index model. Plots E(rm) against E(ri)
is a constant (the intercept), is a random component where if CAPM
holds = slope
Steeper Graph = Riskier Asset (Systematic Risk)
Further Points = Volatile (Firm Specific Risk)
Characteristics of the SIM
sum of the weighted betas
sum of the weighed E(r) on individual assets
Variance of the portfolio
CAPM SIM
Eq. Model, assume MP is efficient Factor Model
Relationship between ’s Realized returns (usually)
Sensitivity factor based on unmeasurable
MP
Sensitivity factor based on observable
market index
Assume = 0 for all securities not necessarily = to
MULTI FACTOR MODEL
Models of returns that respond to several systematic factors.
is the return on the jth factor that impacts
is the firm-specific effect for stock i
for , for all i and J
Total risk Systematic risk
Firm specific risk is
Fama and French: three factor model which includes firm size and book-to-
market ratio.
SMB: Returns on size (small-big) HML: book to market (high-low)
EFFICIENT MARKET HYPOTHESIS
make markets efficient: 1)Timely and accurate disclosure of information 2) Institutional
participation: Research and economies of scale (3) Competition defeats conventional trading
strategies (4) Insider trading regulation and enforcement. Insider trading (1) information
incorporated more quickly (2) Greater information asymmetry - May lead to larger spread,
higher volatility, and lower liquidity (3) Insider trading discourages research and information
production (4) Insider trading discourages market participation - If information asymmetries
are extreme, people simply will not trade. (5)If unregulated, insider trading may be
detrimental to the company and its shareholders. EMH: stock prices reflect all available
information Weak-form: price reflects all past trading info (price, volume) [Empirical
evidence supports] Semi-strong: price reflects public info on the firm (accounting info) [EE
supports] Strong-form: price reflects all public & private info known to investors [EE doesn’t
hold, if true prices would reflect all info, insider traders can’t earn excess returns]
Implications Stock analysis: Both are based on public info so neither should generate excess
profits 1. Technical analysis: focuses on stock price patterns & proxies for buy/sell pressure in
the market – weak-form, semi strong, strong. 2. Fundamental analysis: focuses on
determinants of underlying value of firm (current profit & growth prospects) use economic
and accounting information (and any other publicly available info) and models to predict
stock prices. Portfolio Managers: 1. Identifies risk/return objectives for portfolio given
investors constraints 2. Tailors portfolio to meet investor’s needs, which requires client’s
return requirements & risk tolerance 3. Examines investor’s constraints (liquidity, time
horizon, taxes) Barriers to EMH – Limit to arbitrage – model risk, Noise trader risk,
Implementation costs, behavioural biases. Are markets efficient? Weak-form tests: Pattern in
Stock Returns (short term (momentum effect and long term reversal effect). Semi String
tests – Market anomalies: Patterns of returns contradicting EMH. P/E effect Portfolios with
low P/E exhibit higher average risk adjusted returns than high P/E stock. Eg. Post
announcement price drift. Implications: Portfolio Management: Takes a lot to beat the
market, Passive investment – buy and hold diversified portfolio.
SCL – CML - SML
Examples
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Direct search: buyers and sellers seek each other out directly [gumtree] Brokered: 3rd party assistance in locating buyer or seller [real-estate] Dealer: 3rd party acts as intermediate buyer/seller [primary market] Effective costs of trading: bid-ask spread, brokerage fees, transaction costs, Bid-ask spread: bid: what the broker is willing to buy at, ask: broker sell at. Market order: buy/sell orders to be executed immediately at the best price. Limit buy order: order specifying price investor is willing to buy a security. E. g. buy a certain number of shares when the price goes below x. Limit sell order: order specifying price investor is willing to sell a security. E. g. sell a certain number of shares when the price rises above x. Stop loss order: the stock is to be sold if its price falls below a certain level to stop further losses.
