Calculation - Investment Flashcards
Joe bought stock @ 50, on 75% initial margin. Price fell to 40. What’s new margin position?
68.75
Bob bought stock at $50 per share, on initial margin 75% and maintenance margin 25%. What price is the margin call?
16.6667
B bought stock @ 50, on 75% initial margin and maintenance margin 35%. Price fell to $15. How much equity B must contribute?
2.75 per share
Assume SP mean return is 10%, SD 17%. What’s the probability of return less than -7%, -24% and -41% ?
16%, 2.5% and 0.5%
Calculate SD of stock A and B.
A return: 10%, 13%, 8%, -2%, 14%
B return: 6%, -3%, 4%, -5%, 7%
Which one is more risky?
A: 6.3875%
B: 5.4498%
A
Stock A: SD = 12%, Average Return = 10%
Stock B: SD = 8%, Average Return = 5%
Which one is more risky?
What formula to use?
Coefficient of Variation: SD / Average Return
Higher CV more risk
How does Covariance measures the interactive risk of 2 securities?
How price moves from 1 security in relation to the other.
Cov 1-2= SD1 * SD2 * Cor 1-2
Correlation Cor/ Correlation Efficiency
Measures what and how it’s measured?
Cor = (Cov 1-2) / ((SD1)(SD2))
+1 means 2 assets perfectly correlated, No diversification
0 means there is no relation between 2 assets
-1 means they are perfectly correlated
Diversification starts when Cor < 1
Beta measures what and how it’s measured?
It measures 1 security risk relative to the market.
Beta of bench market risk is: 1
If security Beta > 1, it means it’s more riskier than the market.
If its Beta < 1, it’s less riskier than the market.
Beta vs. SD, what’s the difference in measurements?
Beta measures Systematic, market risk
SD measures total risk
Beta1= Cov 1-m / (SD m ^2)
Or
Beta1= (Cor 1-m * SD1)/ SD m
Beta = R 1 / R m
CML Capital Market Line
How is it relate to CAPM? What does it measure?
It’s the macro aspect of CAPM
It’s the relationship between risk and return of ALL possible portfolios.
It’s NOT used to evaluate 1 security
It uses SD in calculation
SML Security Market Line
What does it measure and how is it different from CML?
It measures the risk and return as defined in CAPM formula.
If Rp > SML, it’s under valued, buy signal
If Return of portfolio < SML, over valued, do not buy
SML uses Beta, CML uses SD
SML calculation
Same as CAPM because it uses the same variables
Re = Rf + Beta(Rm-Rf)
If Rf is 3%, Beta is 1.5, market premium is 9%, what’s the Re (Expected Rate of Return)
16.5%
What’s Information Ratio measuring?
It measures Portfolio performance
Relative risk adjusted performance
It measures the excess return provided by a fund manager, relative to a benchmark. Higher IR the better.
IR = ( Rp- Rm)/ SD a
SD a is annualized SD
Large cap fund increased 12% while SP 500 increased 9.5%. Annualized SD is 15%
What’s the Information Ratio?
0.1667
Treynor Index
What does it measure?
It measures how much return was achieved per unit of risk defined by Beta.
Tp=(Rp - Rf) / Beta p
Which fund would you recommend? Use Treynor Index
Growth Fund: Beta 1.2, Rf 3%, actual return 12%
Index Fund: all same except actual return is 9%
0.075 vs 0.06
Sharpe Index
What does it measure?
It measures return per total risk, thus SD.
Sharpe = (Rp-Rf)/SD
Higher Sharpe the better
Jensen ‘s Alpha
What does it measure? How it measures it?
It measures Portfolio Managers performance.
Alpha = Rp - SML/CAPM
Rp - ((Rf+Beta p (Rm-Rf))
+Alpha means manager did better than market
-Alpha means manager did worse than market
D’s mutual fund returned 19% last year with Beta 2. Risk free 3%, market return 8%. SD 18%. What would you tell D about the performance? What ratio would you use and why or why not.
Can not use Treynor, Sharpe because there is not enough data for comparison assets. Jensen but Jensen is more straight forward.
R^2
When a portfolio is considered diversified
What ratio to use to judge performance
> 0.7 means more diversified, Beta, Treynor, Jensen should be used to measure recommendations
If it’s < 0.7, not diversified, SD, Sharpe should be used
Which fund would you recommend?
A: SD 12%, R^2 0.92, Alpha 2, Shape 1.2
B: SD 13%, R^2 0.90, Alpha 1.8, Sharpe 1.5
Since R^2 > 0.7, use Jensen or Treynor
Mutual fund r^2 0.64, which ratio is appropriate to measure the performance?
Sharpe because r^2 < 0.7
Holding Period of Return based on Cash Flow
Formula
(Ps - Pp +/- Cashflows) Pp
BJ bought a stock $20 on initial 60% margin, paid 10% interest annually, sold 1 year later. What’s his HPR?
77%
HPR Based on Rates of Return
HPR = ((1+r1)(1+r2)…(1+rn))-1
Calculate HPR
Jan 1.9%
Feb 2.3%
Mar -1.5%
Apr 1.7%
May 2.75%
Jun 3.6%
0.1116
What’s the arithmetic mean for the following returns: 6%, 11%, -3%, 13%, 4%
6.2%
What’s average stock price of X, Y, Z
$12,$15,$27
18
Geometric Mean
What does it measure
Time weighted compounded rate of return
((1+r1)(1+r2)…(1+rn)^(1/n)-1)* 100
What’s the Geometric Mean of the following return?
12%
5%
-2%
4.8442%
Bob purchased 1 share of DIS @$50. One year later, stock paid dividend $4 and he bought additional share @$65. He sold the stock for $75. What’s the time weighted return on DIS?
26.5398
Dividend Discount Model
Aka
Intrinsic Value model
What does it measure
Value a company stock by discounting the future stream of cash flow
V = D1/(r-g)
D1=D(1+g)
r=D1/P +g
What’s the intrinsic value of the stock that pays $3.25 Div. Market price $45, growth 6%. Your investor requires 11% return on all investment.
If he buys at market price, what’s Re?
Is the value over or under valued?
68.9
0.1366
Current div is $2. Five years ago div was$1.36. Expect same growth. Required return is 12%. Expected return on market is 14%. What’s the value of the stock?
54.28
PE Ratio
What does it measure
Price per Earning
How much investor is willing to pay for each dollar of earning
It’s useful to evaluate stock with no dividend
P/E = P per share / EPS
Corp A has EPS of $3, stock price at $40, what’s P/E?
13.3333
Stock trades at $50, P/E is 20. What EPS?
2.5
EPS $3, P/E is 20. What’s the price?
60
PEG Ratio
What does it measure
P/E compares to past 3-5 year performance
PEG=p/E / 3-5 growth rate in earnings
PEG =1, fairly valued
PEG >1, fully or over valued
PEG<1, under valued
Book Value
What does it measure?
How much would shareholders receive if company liquidated
If stock > book value, it’s over valued
Div Payout Ratio
What does it measures
Amount of Earnings paid to shareholders in dividends relative to EPS
DPR = Div / EPS
What’s Div Payout Ratio? What’s ROE?
EPS $2
CS div $1
PS div $0.5
Sales $5,000,000
Shares outstanding 1,000,000
Total equity $7,000,000
50%
28.5714% ( EPS / Stock price per share)
Dividend Yield Formula
Div/stock price
Compare to EPS, if less there’s room to increase div
Which company has room to improve div?
A Div yield 10%, stock $20, EPS, $2
B 12%,$40, $5
B
TEY
2 formula
TEY = Tax exempt yield / (1-margin rate)
TEY = Corp rate x (1-margin rate)
Which one to recommend:
Corporate 8.5%
Municipal 5.25%
Corp
Coupon Rate calculation
Coupon pmt / par
Current Yield
Coupon payment/ price of bond
Bond pays $100 per year, what’s the coupon rate?
10
What’s the current yield?
Bond pays $100 a year current price $876
11.4155%
Coupon Rate calculation
CY 8%
Price $900
7.2
What’s YTM?
Bond pays 10% annual, market price $876, 5 years to maturity, pay at par.
13.4894
What’s YTM?
Bond sells at 5% discount to par, paying 11.25% interest, mature in 7 years
12.3371
What’s YTC?
Bond price $1200
Interest 12%
Mature in 10 years
Callable in 5 at $1050
7.9135
Formula to use to estimate Bond Price
D duration
Y YTM
^y Change in Interest Rate
^P/P % Price change
Bond 5 year to maturity, 6% coupon, YTM 8%, selling at $920.15. Duration is 4.4. What’s the new price if rate increase by 0.5%?
938.9211
Convertible Bond Formula
Conversion Value = 1000/Conversion price * Pstock
What’s the conversion value of this bond, bought $1050, conversion price $40, market price $35?
875
Property Valuation
Value = NOI / Cap Rate
Cap Rate = Required Rate of Return
NOI= NI + DEP + MORTGAGE INTEREST
NI = EFF GROSS INCOME - OPERATION EXP
EFF GROSS INCOME = GROSS INCMOM * (1- Vacancy)
GROSS INCOME = RentsUnitsLength
Tripped owns 20 condo, tents for $9167, with 20% vacancy rate. Total expense is $1500000, debt servicing $250k a year, $200k for principal and $50k interest expense. 10% required rate of return. How much would an investor be willing to pay for the property?
5,300,720
