BUAD327. Session 11
Quiz Prep
To Participate in Polling
PollEv.com​/davidhomard008
Test Breakdown
65% Problems (15 points each)
35% Multiple Choice (7 points each)
20 Total Questions
For the problems:
Some “gateway” problems
Some “hinged” questions
Holding Period Return
 P  CF
P
HPR 
P
1
0
1
0
Where:
P1 = Ending price
P0 = Beginning price
CF1 = Cash flow distributions during the period
Real vs. Nominal Returns
Fisher effect: Approximation
nominal rate  real rate + inflation premium
R  r + i or r  R - i
Example: R = 2.8%, i = 0.5%
r  2.8 – 0.5 = 2.3%
Fisher effect: Exact
r = (R - i) / (1 + i)
r = (2.8%-0.5%) / (1.005) = 2.29%
Effective Annual Rates
rannual = ( 1 + rperiod ) c - 1
For c:
Days = 365 / # of days
Weeks = 52 / # of weeks
Months = 12 / # of months
Years = 1 / # of years
Characteristics of Probability Distributions
1) Mean: most likely value
2) Variance or standard deviation: spread around the mean
Standard deviation is square root of variance
3) Skewness: how skewed around the mean
• If skewness >0, positively skewed (longer right tail)
• If skewness < 0, negatively skewed (longer left tail)
4) Kurtosis: how fat are the tails
• A normal distribution has expected value ratio of 3 (the benchmark)
• Kurtosis can be positive or negative (stock market is positive)
Annualizing Standard Deviation
If you are measuring standard deviation in periods other than years, to
convert to annual standard deviation:
Daily – standard deviation * square root (250)
Weekly - standard deviation * square root (52)
Monthly - standard deviation * square root (12)
Excel is =SQRT()
Scenario Analysis – Computation of Expected Return and
Risk of a Recession
Mean return = Spi*Ri
Mean return m = precession* Rrecession+ (1-precession)* Rnorecession =
Variance = precession (Rrecession – m)2 + (Rnorecession – m)2
St.Dev. = SQRT(Var) =
Note: In the computation of variances it is better to convert all percentages
into decimals
Value at Risk Sample Calculation
VaR (1%, normal) = Mean – 2.33SD
Mean = 0.06%
Standard Deviation = 1.20%
Portfolio Value = $500,000
VaR (1%, normal) = 0.06% - 2.33* 1.20%
VaR (1%, normal) = 0.06% - 2.80%
VaR (1%, normal) = -2.74% or -$13,700
Value at Risk Sample Calculation
VaR (5%, normal) = Mean – 2SD
Mean = 0.06%
Standard Deviation = 1.20%
Portfolio Value = $500,000
VaR (5%, normal) = 0.06% - 2 * 1.20%
VaR (5%, normal) = 0.06% - 2.40%
VaR (5%, normal) = -2.36% or -$11,800
Types of Orders
Market Order
•
•
•
•
Specify the security and number of shares
Fills quickly
The indicated bid or ask is for a certain number of shares, so fill prices may
differ from the indicated price if the number of shares is greater
Generally, not an issue for stocks with high liquidity
Types of Orders
Price – Contingent Order
Limit Order
•
•
•
Execution of order is contingent on the price being below the bid for a buy
order or above the ask for a sell order
Could execute immediately or take days or weeks
Trader indicates the time that the order is in effect
o
o
Good Till Day – Trader specifies what day the order expires
Good Till Cancelled – Trade is active for up to 180 calendar days
Types of Orders
Price – Contingent Order
Stop Order
•
•
An order to buy or sell once the stock has traded at or through a certain
price
After reaching the stop price it becomes a market order
o
o
•
Buy stop entered at a price above current price
Sell stop (“stop-loss” order) entered below the current price
Reference https://www.schwab.com/learn/story/3-order-types-market-limitand-stop-orders
Leverage
Buying on Margin
•
•
Investor funds the account (margin) and borrows from the broker against
those funds.
Margin amount is set by the Federal Reserve Board under Reg T
o
o
o
•
•
Current margin requirement is 50%
If you have $5,000 in a margin-approved account, you could buy up to $10,000 of
marginable stock. The $10,000 is referred to as your buying power.
During the crash of 1929, the margin requirement was 10%
The money borrowed is charged interest monthly
If the margin falls below a set amount (maintenance margin), the broker can
issue a margin call or sell your securities (force sale).
Leverage
Buying on Margin
•
•
•
•
Margin $5,000 / Loan $5,000
Initial Stock Price $50
Closing Stock Price $75
Assume 10% total interest on loan
Non-margined account:
Margined account:
Buy 100 shares for $5,000
Sell 100 shares for $7,500
Buy 200 shares for $10,000
Sell 200 shares for $15,000
Profit of $2,500 or 50% ($7,500 - $5,000) / $5,000
Profit of $4,500 or 90% on margin amount
((Investment Value – Loan – Interest) – Margin) /
Margin
Leverage
Calculating Margin Call
•
•
•
•
Purchase stock for $50
200 shares purchased with 50% margin ($5,000 margin, $5,000 loan)
Maintenance Margin: 30%
At what stock price do you receive a margin call (P)?
• Shares(P) – loan = Maintenance Margin
Shares(P)
•
200(P) - $5,000 = .3
200(P)
200(P) - $5,000 = 60(P)
-$5,000 = -140(P)
P = $35.71
Regulation
Insider Trading
•
•
Trading on material, non-public information by officers, directors or major
stockholders
This includes passing on material, non-public information to outsiders
o
•
•
Both parties may be prosecuted
Insiders may trade the stock but must file Form 4 within 2 business days.
Corporate insiders are generally prohibited from trading their stock from the
end of the fiscal quarter until after the earnings release (blackout period)
Capital Allocation Line - CAL
E(Rp)
E(Rc)-rf=6%
Slope = E(R) – rf
sp
rf = 2.5%
0
s
A Simple Utility Function
Mathematical form:
U(P) = E(Rp) - 0.5A*sp2
If:
E(Rp) = 12%
sp = 17%
A= 3
U(P) = .12 - 0.5*3*.172 = .12 – .043 = .077
Two-Security Portfolio: Expected Return
Weighted average of securities expected returns:
E(Rp) = wA*E(RA) + wB*E(RB)
wA + wB = 1
Amethyst Inc.: E(RA) = 15%
Beryl Co.: E(RB) = 20%
Diversification and Portfolio Risk
Why end at two stocks (or bonds or ETFs, etc.)?
Diversification is a strategy where you consider different stocks, ETFs or
asset classes to minimize the volatility of the portfolio.
Risk that can be diversified away is also known as nonsystematic risk,
unique risk or firm-specific risk
Risk remains after extensive diversification called systematic or
nondiversifiable risk.
Risk in Portfolios
24
Global Minimum Variance Portfolio
 The portfolio of two risky securities with the
lowest possible risk
 Formula for the weights:
𝜎𝐵2 − 𝜎𝐴𝐵
𝑤𝐴 = 2
𝜎𝐴 + 𝜎𝐵2 − 2𝜎𝐴𝐵
wB = 1 - wA
Global Minimum Variance Portfolio - Example
Data
Amethyst Inc.: E(Ra) = 15%, sa = 30%
Beryl Co.: E(Rb) = 20%, sb = 50%
r (Correlation) = -1
Calculations of weights
Cov(A,B) = -1*0.3*0.5= -0.15
wA = (0.5^2 + 0.15)/(0.3^2 + 0.5^2 + 2*0.15)
wA = 0.40/0.64 = 5/8 = 0.625
wB = 0.375
s  s AB
wA  2
s A  s B2  2s AB
2
B
Global Minimum Variance Portfolio - Example
Calculations of expected return and risk
wA = 0.79
wB = 0.21
E(Rp) = 0.79*0.15 + 0.21*0.2 = 16.05%
sp2 = wA2sA2 +wB2sB2 +2wAwBsAB
Var(p) = (0.79*0.3)^2 + (0.21*0.5)^2 + 2*0.79*0.21*0.03 = 0.08
Minimum Variance Frontier
E(r)
Efficient
frontier
Global
minimum
variance
portfolio
Individual
assets
Minimum
variance
frontier
Beta – Estimating
You can estimate Beta if you know the standard deviation of the market,
the standard deviation of the asset and the correlation between them.
  r*sa
sm
Sample Questions
In the book:
Page 89: Questions7, 9, 10
Page 90: Questions 14, 15
Page 91: Question 2
Page 125: Concept Check 5.2
Page 155: Questions 7, 13
Page 156: Questions 2, 3
Page 157: Question 7
Sample Questions
In the book:
Page 162: Concept Check 6.1
Page 182: 13, 21
Page 184: 1
Page 208: Concept Check 7.3 (b, c,d)
Page 221: 4
Page 224: 4
Page 225: 10
Page 226: 12a, 13a, 13b
Page 273: 3, 4
Formulas Provided (on last page of quiz)
𝜎𝐵2 − 𝜎𝐴𝐵
= 2
𝜎𝐴 + 𝜎𝐵2 − 2𝜎𝐴𝐵
= wA2sA2 +wB2sB2 +2wAwBsAB
 r*sa
sm
= E(Rp) - 0.5A*sp2
= Mean – 2.33SD
= Mean – 2SD