Inv in Eq Final
How do hedge funds differ from Mutual Funds
- Income requirements and minimum investments - Lockup periods - Investment strategies - Fee structure
Asymmetric Information
- a transaction between economic agents when the parties do not have access to the same information
Implementation challenges
-Alpha estimates are frequently noisy -Selection and survivorship bias -Beta may be misestimated (think Bloomberg adjustment)
Jensen's alpha - risk adjustment:
-Alpha measures return in excess of an investment's required risk premium, under the assumption that the model correctly measures the risk premium *Risk-adjustment argument for multifactor models is weaker because it is less clear that they capture risk
Behavioral explanations?
-An explanation in time A. Some good news comes out B. Some investors (but not enough) react to the news driving prices higher (underreaction) C. Others slowly realize that this is really good news and continue to buy (price goes up). There is a large amount of excitement so they buy as well (Overreaction) D. Result-- is that the price drifted too high >They will later correct *If momentum is due to overreaction then long-term returns should be negative (long-term reversal)
Fee structure of Mutual funds
-Charge a fee for assets under management -Back-end and front-end loads -No performance based compensation
Discounted cash flow models
-Dividend discount model -Free cash flow to equity model -Free cash flow to the firm model -Adjusted present value (APV) model -Economic value added (EVA) model
Risk?
-Hard to come up with a risk-based story for momentum -Fama-French model cannot explain momentum returns -However, momentum does not represent risk-free profits
Data mining?
-Has been widely publicized since 1991, Yet momentum profits still exist Data mining does not seem to explain momentum -
Momentum Summary
-Historically, Momentum has done great (up to 12% per year) -Most agree it does not relate to standard notions of systematic risk. But it is not riskless in the sense of being a sure thing - There are some behavioral explanations. But no consensus on an Answer - Industry knows not to ignore momentum, even though it is not a fully understood phenomenon
Two "building blocks" of behavioral finance:
-Investor Psychology -Limits to Arbitrage
Pick between the options in choice 1 and then choice2: Choice #1: A: 100% chance of winning $240 B: 5% chance of winning $0 25% chance of winning $1000 Choice #2: C: 100% chance of losing $750 D: 75% chance of losing $1000 25% chance of losing $0 Then consider choice 3: Choice #3: E: 75% chance of losing $760 25% chance of winning $240 F: 75% chance of losing $750 25% chance of winning $250
-Many people choose A (i.e., the sure gain) and D (i.e., the chance of losing nothing) -Clearly here in Choice #3, F dominates E (i.e., F is like E plus an additional $10). However, it is easy to show that: E = A + D F = B + C
Style analysis -Introduced by William Sharpe
-Regress fund returns on indexes representing a range of asset classes -The regression coefficient on each index measures the fund's implicit allocation to that "style" -R -square measures return variability due to style or asset allocation -The remainder is due either to security selection or to market timing
CAPM and multifactor regressions decompose returns into:
-Returns explained by exposure to known factors/styles -Unexplained returns (alpha), which could be due to 1. Stock picking 2. Market timing 3. Luck
What does Universe Comparison tell us?
-Risk adjustment: Reasonable approach if comparable funds and benchmark have similar systematic risk -Performance attribution: I could have invested in the index or alternative funds, so maybe relative performance is what I should care about -Luck or skill: Subtracts off common market performance, which is likely due to luck
What does information ratio tell us?
-Risk adjustment: Tells us how much we can increase Sharpe ratio of market portfolio by adding portfolio P -Performance attribution: Not useful -Luck or skill: High information ratio implies alpha is high and tracking error is low; this gives us more confidence that the alpha is real as opposed to luck/noise
What does Treynor Measure tell us?
-Risk adjustment: This is the correct risk vs. return metric if: 1. Fund is part of investor's overall investment portfolio 2. Risk is measured by CAPM beta Performance attribution and luck vs. skill: Improvement over Sharpe ratio because we adjust for beta but still does not adjust for market returns or exposure to other factors
What does Sharpe Ratio tell us?
-Risk adjustment: This is the correct risk vs. return metric if: 1. The fund represents investor's entire investment portfolio 2. Investor is one-period mean-variance optimizer (CAPM assumptions) -Performance attribution: Not much value -Luck or skill: Not much value
Universe comparison
-Simplest and most popular way to adjust returns -Compare returns to benchmark and universe of similar funds ex: "fund beat its benchmark each of the past three years" or "Fund consistently performed in the top quartile"
Performance evaluation methods
-Universe comparison -Sharpe Ratio -Treynor Measure -Jensen's alpha >With CAPM >With 3-factor model, 4-factor model, 5-factor model -Information Ratio
typically a segment of a larger financial institution (e.g. Goldman Sachs) will include
-Wealth management -Proprietary trading -Brokerage services -M&A structure and consulting
What you learn from style analysis?
-What is the fund's actual investment style? -How closely do the funds returns track its investment style? -What is the fund's style-adjusted performance
Relative valuation
-cross-sectional comparison -time-series comparison
Determinants of Firm Value Under the dividend discount model:
-dividend per share -discount rate -growth rate
Prospect Theory -established Daniel Kahneman and Amos Tversky
-people see situations of potential gains and potential losses differently. >risk averse when gains are involved >risk-seeking when trying to avoid losses (investors are loss averse.)
Questions for today Economist perspective:
1. Can fund managers outperform the market on a risk-adjusted basis? 2. Are markets efficient?
Questions for today Investor perspective:
1. How should I evaluate fund/portfolio performance? 2. Should I invest in actively managed mutual funds? 3. Should I invest in hedge funds? 4. Which funds should I invest in?
Fund or portfolio had high realized returns; we need to ask (at least) three questions
1. Risk adjustment: How risky was the fund portfolio? Were returns compensation for risk or did it exceed the risk premium? 2. Performance attribution: How did the fund/portfolio do relative to other portfolios with similar investment styles? Could I have achieved the same results myself? 3. Luck vs. skill: Is past performance representative of what we should expect in the future?
Suppose a firm pays a current dividend of $1, which is expected to grow at 5% indefinitely. If the current price of the firm's stock is $35, then what is the required rate of return on the stock?
35 = 1(1.05)/k-.05 = .08
3Com & Palm:
3Com spins off Palm division -Palm IPO shares trade for more than 3Com shares, which included rights to an additional 1.5 Palm shares -Valuation indicates that net value of 3Com's business is negative
Investor Psychology
:People make mistakes repeatedly and do not necessarily learn from those mistakes -Processing errors -Behavioral biases
Multistage Model
Allow for dividends to grow at different rates for intermediate period before leveling off to a constant growth rate
Momentum has attracted a huge following on Wall Street. Many people use it to invest. Why has it worked?
Data Mining: special artifact of U.S. data Risk: momentum returns are reward for priced risk Behavioral: Momentum is a form of mispricing
Bottom line: Which measure is best?
Depends on what you are trying to measure
The market consensus is that Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. What price should the stock be trading at?
First find k (Market capitalization rate) k = rf + β[E(rM) − rf] = .06 + 1.25(.14-.06) = .16 Then find the growth rate g = ROE*b g = .09*2/3 = .06 Now find 𝐷1=𝐸0∗(1+𝑔)/(1−𝑏)=$3∗1.06∗(1/3)=(3.18/3)=1.06 Intrinsic value 𝑉0=𝐷0(1+𝑔)/(𝑘−𝑔)=𝐷1/(𝑘−𝑔)=$1.06/(.16−.06)=$10.60
Modelling Firm Value w/ Fundamental Analysis Goal: Options:
Goal: best model for the individual firm Options: -Discounted cash flow models -Relative valuation
Information ratio (appraisal ratio)=
IRp=ap/idiosyncratic stnd dev *Divides alpha by idiosyncratic (residual) standard deviation
Jensen's alpha
Intercept from regression of excess returns on excess market returns (CAPM) or excess market returns and other factors (multifactor model) for 3-factor: -HML book-to-market -SMB return on portfolio
Prospect theory: disposition effect
Investors are more reluctant to realize their losses than they are when taking their gains
Momentum
Jegadeesh & Titman (1993) studied a portfolio investment strategy that exploits lagged adjustment of stock prices to information -They found spread returns of 12% - 15% on average over the entire sample
Present value of growth opportunities (PVGO)
Net present value of a firms future (not currently existing) investments
____________ and _____________ makes evaluating individual funds difficult if not impossible
Noise selection bias
Representativeness: Mary is quiet, studious, and very concerned with social issues. While an undergraduate student at UC Berkeley, she majored in English Literature and Environmental Studies. Given this information, please indicate which of the following three cases is the most probable: a. Mary is a librarian b. Mary is a librarian and an environmentalist c. Mary works in the banking industry
Note that by definition b is less likely than a. There are instances where a is true and b isn't
Current market value $41 per share with earnings of $3.64. What is the present value of growth opportunities (PVGO)? Price= PVGO=
Price = Current earnings/(cost of capital) + PVGO Price = $41 = 3.65/.09 + PVGO PVGO = 41- 40.44 = $.56
Royal Dutch & Shell:
Royal Dutch shares trade separately from Shell shares. -Cash flow of combined company is split 60%/40% between Royal and Shell, but Royal shares don't always trade @ 1.5 multiple of Shell shares
Sharpe ratio=
Sp=(rp-rf)/Stnd dev p Divides average excess returns by standard deviation of returns
Limits to Arbitrage
The actions of rational traders are insufficient to offset the actions of irrational agents -Fundamental risk -Transaction costs -Model risk
Free Cash Flow based valuation
Think of total cash flows available to the firm, rather than just dividend payments FCF - free cash flow FCFF - free cash flow to the firm FCFE - free cash flow to equity holders
Treynor measure=
Tp=(rp-rf)/beta p Divides average excess returns by beta (systematic risk)
Dividend Discount Model
Vo=(D1/(1+k))+(D2/(1+k)^2)+.... V = firm value D = dividend stream k = discount rate (cost of equity capital) Simply discount each cash flow independently (very tedious!)
Constant-Growth Div Discount Model (Gordon Model)
Vo=Do(1+g)/k-g= (D1/k-g) V = firm value Do = dividend in year 0 K = discount rate Can use one simple formula to calculate the value of an infinite sum!
The comparison universe is a benchmark composed of
a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.
Anyone can buy into most mutual funds, but hedge fund investors must be _______________
accredited
Jensen's alpha and Treynor measure are frequently appealing because they....
adjust excess returns for systematic risk (we see if fund generates returns without extra risk exposure)
Hedge fund evidence is more mixed; hedge funds may deliver some ___________, but they also have significant _________________ which may be understated
alpha systematic risk
Market timing involves changing _____________ in response to changing ____________________
asset allocation expected returns *is a form of active investing and requires investor to be able to forecast returns
Fee structure on hedge funds
charge a % of assets under management (1-2%) as well as -Incentive fee (typically 20%) - share any returns beyond a stipulated performance -Water mark
Investment Banking
firms specializing in sale of new securities to the public
The market capitalization rate (cost of capital) for Admiral Motors Company is 8%. Its expected ROE is 10% and expected EPS is $5. The firm's plowback ratio is 60% What is the growth rate? What is the PE ratio?
g = ROE * b = .1*.6 = .06 𝑃/𝐸=(1−𝑏)/(𝑘−𝑔)=(1−.6)/(.08−.06)=20
growth rate=
g=ROE*b g = growth rate ROE = return on equity b = plowback ratio
Hedge funds have more exposure to down markets than up markets - so we should expect _________________
higher returns
Information Ratio is good for identifying....
how much of a given asset to mix with an already diversified portfolio
Fundamental risk:
if you buy a mispriced stock, it will convert to intrinsic value, but maybe not in your time window market fundamentals change while you hold your position "Market can remain irrational, longer than you can stay solvent" - Keynes
A hedge fund with $1.8 billion of assets charges a management fee of 3% and an incentive fee of 20% of returns over a money market rate, which currently is 6%. Calculate total fees, in dollars, if the hedge fund generates portfolio returns of 12%:
incentive fee= .2x(.12-.06)x$1.8b=$21.6m AUM fee= .03x$1.8b=$54m Total fees= 21.6m+54=75.6m
Representative bias
is judgment based on stereotypes. These are "shortcuts" that people commonly use to help process large amounts of information quickly **Can also mean we attribute too much weight to small samples
Mutual funds are limited in the amount of _________________ and the amount of _______________
leverage they can take on short sales they can make
Survivorship bias
means we have data only on those funds that did well
-Investors who selected A & D when they were offered separately would not make the same choice when the alternatives are packaged together. This is a special type of framing called __________________
mental accounting
moral hazard
occurs when one person takes more risks because someone else bears the cost of those risks.
Often, hedge funds will require large minimum investments of _________________
over $250K-$1M
MF are also restricted from having too large of an ______________
ownership in any one asset
Dividend payout ratio
percentage of earnings paid out as dividends
Water mark
previously attained value that must be re-attained before any incentive fee can be earned
Plowback ratio/Earnings retention ratio -
proportion of a firm's earnings that is reinvested in the business (not paid as dividends) 𝑃/𝐸=(1−𝑏)/(𝑘−𝑔)
Framing
refers to the possibility that the choice that an investor makes in a certain situation depends on how the investment is presented or "packaged" (i.e., framed)
Model risk:
reluctance to trade on a strategy b/c you may be wrong
Asset allocation:
skillfully assigning portfolio weights to different asset classes ex: -my fund is 60% equities and 40% T-Bills -The benchmark is only 50% equities -I am overweight in stocks (relative to benchmark) because I believe stocks will outperform bonds on a risk-adjusted basis
Security selection:
skillfully picking specific securities within an asset class ex: -my fund is 50% in equities -My equity return is 15%, the market return is only 12% -I picked stocks that performed better than the market
Bubbles:
stark deviation from fundamental values, usually followed by large crash -Hard to identify ex-ante
Behavioral Finance
the study of how investor/trader psychology affects financial economic judgments and choices
On average, mutual funds _________________ the market by about 1% per year
underperform *Past good performance is mainly due to luck and tends not to persist
Sharpe Ratio's measure of risk is __________, so its appropriate for...
variance evaluating overall portfolio performance, not so much individual investments
Hedge funds have ______________ on the strategies they can use
virtually no limitation *can use whatever leverage the market will give them and no limit on short sales (e.g. LTCM)
The market consensus is that Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. Calculate the P/E ratio
we can either calculate the Leading PE - using next period earnings - or trailing PE - using current or most recent earnings Leading = 10.6/3.18 = 3.33 Trailing = 10.6/$3.00 = 3.53
Lockup periods
where hedge funds are able to lock up an investor's money for a period of time, during which the investor is unable to redeem his or her shares -Typically the first 2-3 years of a new investment
a firm pays a $1 dividend today. This dividend is expected to grow 50% per year for 3 years and then at 5% thereafter. What is the current stock price if the cost of capital is 10%?
𝐷1=1(1.5)=$1.50 𝐷2=$1.50(1.5)=$2.25 𝐷3=$2.25(1.5)=3.375 𝑃3=𝐷4/(𝑘−𝑔)= (3.375(1.05))/(.10−.0)=3.54/.05=$70.88 𝑃0=(1.50/(1.10)^1)+(2.25/(1.10)^2)+((3.375+70.88)/(1.10)^3) 𝑃0=1.36+1.86+55.79=$59.01
The market consensus is that Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. Calculate the present value of growth opportunities
𝑃0=(𝐸1/𝑘)+𝑃𝑉𝐺𝑂 𝑃𝑉𝐺𝑂=𝑃0-(𝐸1/𝑘)=10.6−(3.18/.16)=−9.28
The market consensus is that Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. Now suppose the plowback ratio changes to 1/3, what would the new price be?
𝑔=𝑅𝑂𝐸∗𝑏= .09∗(1/3)= .03 𝐷1=𝐸0∗(1+𝑔)/(1−𝑏)=3∗(1.03)*(2/3)=$2.06 =v0𝐷1/(𝑘−𝑔)=𝐷1/(.16−.03)
