Class notes Flashcards
What are 2 investment objectives
Return
Risk
Investment constraints
Time Horizon
Taxes
Liquidity
Legal
Unique circumstances
Investment Policy statement has 2 categories
-Investment Ojectives
-Investment Constraints
Absolute return example
Client wants to hit 5% return every year
Relative Return
benchmarking against something
ex + or - 1% of the S&P 500
Goals based return
ex retiree shouldn’t focus on the S&P 500 - focus on the rate of return that makes you successful for the things you want to achieve
2 Factors regarding risk
Ability - based on financial situation
Willingness - how comfortable are you
THESE MAY CONFLICT
If a retiree has sufficient pension/SS - how does that affect their risk regarding other assets
they should be more willing to take on risk with their other investments
σ or Sd
standard deviation
k or r
required return
N or T
time periody
y or i
market rate of interest
α or a
Alpha
β or B
Beta
b or r
retention ratio
Rf or rf
risk free rate
ρ or r
correlation coefficient
2 things a company can do with its earnings
-pay to shareholder as dividend
-retain and reinvest back into company
Payout ratio
total dividend / total earnings
or
DPS/EPS
Retention ratio
retained earnings/total earnings
OR
1- payout ratio
Retention ratio and payout ratio have to add up to what
1
Company’s policy is to retain 75% of earnings. Earnings per share were $10 what is Dzero?
$2.50
g = ROE x b
Dividend growth rate where:
g = dividend growth rate
ROE = return on equity
b = earnings retention rate
1-b = dividend payout ratio
Return on equity is a company doing what
reinvesting the money they make back into the company
Who might have a higher return on equity, google or target?
Google more likely because they’re a growth company whereas target is more established and stable - target would pay a dividend
A firm pays a dividend of $1.20, has return on equity ROE of 15%, reports total earnings per share of $6. What is the firm’s sustainable growth rate? g?
Calculate the payout ratio
1.20/6 = .2
Calculate the retention ratio
1-.2 = .8
Calculate g = ROE x b
.15 x .8 = .12 or 12%
Dzero is what vs Done
Dzero is current dividend, Done is next year’s dividend
Intrinsic value formula uses what year’s dividend?
next years
Next year’s dividend (D one) formula
D zero (1 + g) where D zero is this years dividend and g is the growth rate
If you have Dzero and the growth rate, how would you find Dthree if the growth rate is 10%. Dzero is 1.50
Dzero ( 1+ g)
1.50(1.10) = D one
D one (1.10) = D two
D two (1.10) = D three
Tip: DO A TIMELINE
A firm currently pays a dividend of $3.30 and expects that to grow at a constant 7%. The stock’s required return is 11% What is the intrinsic value of the stock?
Remember they gave you D zero you need D one
V = D one / r - g
V = (3.30 * 1.07) / .11 -.07
V = 3.5310 / .04
V = $88.275 = $88.28
88.28 is the value we think the stock is worth based on our required return
If the stock is trading at 92 - should you buy it?
No
Stock Yield Formula
D one / P
D one = next year’s dividend
P = current price
Stock has an expected return of 8% and your client’s required rate of return is 7% do you buy the stock?
Yes
Current Dividend has been paid or not?
Yes, current dividend has already been paid. Sometimes referred to as last year’s dividend
What is the risk free rate based on?
yield on 90 day T Bill
Market RIsk Premium
Rm - Rf
If you’re given Market Risk Premium you don’t need to then subtract the risk free rate, it’s already been subtracted
Rm - Rf is also called
Market Risk Premium
XYZ Co
Current Dividend = 2.20
Current EPS = $11
ROE = 10%
Beta = 1.25
Firm expects constant dividend and earnings growth rate of 8%
If the market risk premium is 8% and and the 90 Day T Bill rate is 4% what is the co’s intrinsic value?
V = D one / r - g
V = ($2.20 * 1.08) / r - .08
You need R - they gave you Rm-Rf when they gave Market Risk Premium
R = Rf + (Rm - Rf) B = .04 + (.08)1.25 = .14 or 14% SO
V = (2.20 * 1.08) / .14 - .08
V = 2.376 / .06 = $39.60
If they hadn’t given g you could do
g = ROE x b where b is the retention ratio
payout ratio is DPS/EPS = 2.20/11 = .2
Retention ratio = 1 - b = .8
.1 * .8 = .8 or 8%
Jensen’s Alpha
A = Rp - [Rf - (Rm - Rf) Bp
A = Rp - [Rf - (Rm - Rf) Bp
A = Jensen’s Alpha
Rp = realized return on portfolio (this will be given)
Rf = risk free
Rm = return of the market
Bp = beta
NOTE everything inside the brackets is just required return or CAPM
Another way of saying Jensen’s Alpha
portfolio return minus CAPM
When there’s a line above a letter in an equation what does that mean?
Realized - we’re looking at backwards looking actual numbers - not future projections
If realized return is higher than the required return the Alpha is?
Positive
If the realized return is lower than the required return the Alpha is?
negative
Rsquared > 70 you would use what
Beta, alpha, traynor
Rsquared is < 70 you would use what
Standard deviation based like Sharpe ratio
Standard Deviation measures what
how much, on average, an investment’s return varies or deviates from the mean return
Variance measures what
the average distance between each of a set of investment returns and their mean value
What is standard deviation squared?
Variance
ABC stock has returns over the last 4 years of: 12%, 18%, -2%, and 6%. Calculate the standard deviation.
12 E+ (weird e plus key)
18 E+
2 CHS E+
6 E+
G x (zero key) gives mean 8.5
G s (decimal key) gives standard deviation 8.544
What percent probability will the actual return fall within 1 standard deviation?
68%
What percent probability will the actual return fall within 2 standard deviations?
95%
What percent probability will the actual return fall within 3 standard deviations?
99%
If you have a mutual fund with average return of 8% and standard deviation of 6 - where would you expect returns to fall in 95% of the time?
returns fall within 2 standard deviations 95% of the time so it would be
-4% and 20%
If you have a mutual fund with average performance of 8% and a standard deviation of 6%, what percent of the time would you expect a return of 2% or higher?
2% is one standard deviation below.
You know on the bell curve that 68% at the top divides in half, so 1 standard deviation represents 34%. Add that to the other 50% on the other side. 84%
Tail Risk is greater than how many standard deviations?
3 - the .5% on either side of the end of the curve
What market has typically been negatively skewed?
US Stocks
What market typically has been positively skewed?
VC market
Mode is
the most common number to appear in your set of data
Mean is the same as
average
Kurtosis
degree to which bell curves are peaked or flat at the top. High kurtosis data is peaked at the mean, low kurtosis data is rounded at the mean. The kurtosis for normal data is 3.
Leptokurtic
high kurtosis. peaks at the mean, lots of data in the middle. Downside is tail risk is higher
Platykurtic
low kurtosis. rounded at the mean - less rail risk
Kurtosis for normal data is
3
Unsystematic diversifiable risks
Business Risk
Financial Risk
Default Risk
Regulatory Risk
Systematic undiversifiable risk
Market Risk
Interest Rate Risk
Reinvestment rate risk
Purchasing power risk
Exchange rate risk
Does the market reward you for taking on unsystematic risk?
No
How many stocks typically would you need in a portfolio to have it be diversified?
30 - research supports this
Total investment risk is measured how
standard deviation, a statistical measure of variability
Market risk example
everything sells off at once - not much you can do - like 2008 - doesn’t matter how good of a company/investment, everyone was selling bc they needed liquidity
Interest rate risk
broadly the risk of interest rates going up. if you don’t buy bonds do you not have interest rate risk? - no because companies have higher borrowing costs
Reinvestment rate risk
You own investments in a declining rate environment. Say you own a bond from the 80s - was paying 10% - when it matured rates were 4% or 5%. Reinvesting bonds in a bond ladder in a declining rate environment
Inflation risk
the loss of buying power. prices are going up. medical costs, education. need to account for increasing costs in investments and in planning
Exchange rate risk
Dollar strengthens and you had international investments, you could have a loss even though the investment made money.
Unsystematic risks effect
both individual companies and sectors/industries
Business Risk
unsystematic risk - the business model - Blockbuster or Kodak model went bust, they were replaced.
Financial risk
unsystematic risk - how the company is structured. Do you have too much debt, credit quality, enough earnings to pay dividends, do you need to cut dividends?
Tesla using convertible bonds that could be exchanged for equity, diluting shareholder value or bankruptcy
Default risk
can you pay your creditors - do you have enough cash flow. issue as rates go higher. do you bring in enough revenue to cover the cost of debt. Toys R Us took on too much debt/complicated financing
Regulatory Risk
law/government changes - ESG - adapt to new regulations - environmental changes. Uber - are drivers employees or no re: benefits
High credit quality bonds pay higher or lower interest?
Lower interest bc default risk (unsystematic) is lower
Security A has a return of 8% and a standard deviation of 10%, what is the coefficient of variation?
CV = SD/Return
.10/.08 = 1.25
For every unit of return, which there were 8, I have 1.25 units of risk
COVij = Pij Oi Oj
COV = covariance between assets i and j
Pij = correlation coefficient between i and j
Oi = standard deviation of i
Oj = standard deviation of j
Correlation
statistical technique that measures the relationship of one asset to another
Assets that move together have what correlation
positive
Assets that don’t move together have what correlation
negative
Correlation coefficient expressed in what range
-1 to +1
+1 is perfectly positive
-1 is perfectly negative
Does preferred have voting rights?
Not typically - but dividends have a higher % and typically guaranteed to be paid
Dividends guaranteed on common?
No - dividend can be cancelled. Preferred would be paid first
American Depository Receipts
Foreign stocks which trade on a US exchange - Bank buys shares on foreign exchange and then issues ADR version of the shares which are backed by the shares held by the bank
Who owns the stock in an ADR?
The bank that issues the ADR
Prospect Theory
investors fear losses more than they value gains
Date of record
date it is determined who owns stock in the company and is entitled to receive a dividend
Date of declaration
Date the board approves and decides to pay a dividend
Ex dividend date
date the market price adjusts for the dividend
If portfolio A has a correlation of +1 to Portfolio B and portfolio A returned 10% what would we expect portfolio B to return?
10%
If portfolio A has a correlation of -1 to Portfolio B and portfolio A returned 10% what would we expect portfolio B to return?
-10%
Portfolio A returns 7% and portfolio B has a correlation of .75 what would we expect B to return?
.07 * .75 = 5.25%
If you are given correlation in a standard deviation of 2 asset portfolio - what will you need to calculate?
Covariance
Beta formula is
correlation * standard deviation
_____________________________
standard deviation of the market
Most common Beta question example will ask about
A stocks performance to the market most likely S&P 500
Market by definition has a Beta of what
1
Betas > 1 have what volatility compared to the market
more volatile than the market
Beta < 1 have what volatility compared to the market
less volatile than the market
What is a defensive beta?
Less than1
Stock A has a beta of 1.25 and the market return is 10% what is the return of stock A?
12.5%
Can you use beta to compare other things than stock to index?
Yes
High R squared means the portfolio is what?
Diversified
If you have a decreasing market do you want beta to be high or low?
low
If you have an increasing market do you want beta to be high or low?
High
How can you change your beta?
You can adjust your portfolio weightings to different sectors of the market or different securities
Using coefficient of determination how can you represent unsystematic risk?
1 - R squared
Rsquared or coefficient of determination represents
Systematic risk meaning we can use beta
Portfolio A returned 20 with a standard deviation of 12 and Portfolio B returned 18 with a standard deviation of 8. Risk free rate is 3. What has the better sharpe ratio?
.20 - .03 / .12 = 1.42
.18 - .03 / .08 = 1.875
Always take the higher sharpe ratio
Numerator of sharpe is also called excess returns why?
It’s the return minus the risk free rate, returns outside of risk free
How to remember the sharpe ratio higher the better?
Think of a high point - you want the sharp point high in the air
A 100% bond portfolio has the exact same risk level as what other allocation
30 stock 70 bond
Treynor is the exact same calculation as Sharpe only instead of using standard deviation you’re using what
Beta
Another name for Information ratio
appraisal ratio
Information Ratio
numerator is known as alpha, denominator is standard deviation of alpha not the standard deviation of the portfolio
Do you want a higher or lower information ratio?
Higher - just like sharpe
On a joint account, what is the FDIC coverage?
250k per depositor
30 day t bill also known as what
cash
If a husband and wife each have an individual account and a joint account together, what is the full FDIC coverage?
1 mil
What are some examples of alternative investments?
Hedge funds, private equity, etfs, crypto, digital assets
