High 5 Investment Planning 17% (29 Questions) Flashcards
Covariance Between Two Sample Assets
COV ij = ρ ij σ i σ j
Measures the extent to which two variables (the returns on investment assets) move together, either positively (together) or negatively (opposite).
Covariance = (st. dev #1)(st. dev #2)
Ex:
If Covariance between A & B is 96 and the standard deviation for A is 20% & B is 12%.
What is the correlation between A & B?
96 = (20) (12)pij
96 = 240pij
96/240 = pij
pi = 0.40
Correlation Coefficient (R or p)
(Overall range: +1 to −1)
Measures the extent to which the returns on any two securities are related; denotes only association, not causation; and measures the strength of the straight-line or linear relationship between two variables
-1.0 = Move in opposite directions ↑ ↓
+1.0 = Movement is identical ↑ ↑
0.0 = Security movements are unrelated
EX:
A portfolio manager adds a new stock that has the same total risk as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1.
Adding this stock will have what effect on the total risk of the revised portfolio’s returns?
The standard deviation will:
A. decrease
B. increase
C. decrease only if the correlation is negative
D. cannot be determined
Answer: A.
If the correlation coefficient is < 1, there are benefits to diversification. Thus, adding the stock will reduce the portfolio’s total risk deviation.
Coefficient of determination (R²)
R² is used for two purposes
- To determine if Beta is meaningful.
If R2 is >= 0.70, Beta is reliable.
R² < 0.70 indicates Beta, although calculable, is NOT meaningful
- To select an appropriate benchmark. The most appropriate benchmark for any given portfolio is the benchmark with the highest R² relative to the portfolio
I. Calculated by squaring the correlation coefficient
II. Describes the percentage of variability of the dependent variable (e.g., a stock) that is explained by changes in the independent variable (e.g., the overall market)
III. Calculated by squaring the correlation coefficient b. Describes the percentage of variability of the dependent variable (e.g., a stock) that is explained by changes in the independent variable (e.g., the overall market)
Standard Deviation
Used to measure risk for normal distributions: the greater the standard deviation, the greater the risk (volatility)
68% w/in 1 SD of mean
95% w/in 2 SD of mean
99% w/in 3 SD of mean
Ex:
Returns: (7.3, 4.4, -7.9, -1.2, 6.5, 9.2)
Calculator Steps:
2nd #7 (DATA)
7.3 Enter ↓↓
(you only want to enter on X’s)
4.4 Enter ↓↓
-7.9 Enter ↓↓
-1.2 Enter ↓↓
6.5 Enter ↓↓
9.2 Enter
2nd #8 (STAT)
LIN
↓↓
X̅ = 3.05 (mean return)
SX = 6.44 (Standard deviation)
Systematic Risk
Cannot be eliminated through diversification
SYSTEMATIC: Cannot be eliminated through diversification
(PRIME)
1. Purchasing power risk *Inflation Risk:
the risk that inflation will erode the real value of an investor’s assets
- Reinvestment rate risk: —the risk that proceeds available for reinvestment must be reinvested at a lower rate of return than that of the investment vehicle that generated the proceeds
- Interest rate risk: —the risk that changes in interest rates will affect the value of a security
- Market risk: Risk of price volatility in the overall securities marketplace 2.) Affected by changes in the general economy
- Exchange rate risk: the risk that a change in the relationship between the value of the dollar and the value of the foreign currency during the period of investment will negatively affect the investor’s return
Unsystematic Risk
Diversifiable
Risk that is unique to a single security, business, industry, or country
UNSYSTEMATIC:
Risk that is unique to a single security, business, industry, or country
Business risk: The uncertainty of operating income
Financial risk: The risk that a firm’s financial structure will negatively affect the value of an equity investment
Default risk: The risk that a borrower will be unable to service its debt obligations
Political risk: The risk that the political or economic climate of a country will negatively affect an investment
Investment manager risk: The risk associated with the skills and philosophy of the individual manager of an investment fund or account
Liquidity and marketability risk: Liquidity is the ability to sell an investment quickly and at a competitive price, with no loss of principal and little price concession
Marketability is the ability to find a ready market where the investor may sell the investment
Tax risk: The risk that taxation of investment gains or losses will negatively affect investment return
Capital Asset Pricing Model (CAPM)
Allows an investor to determine an assets expected rate of return & how much risk the investor should assume to obtain a particular return from an investment
*ONLY accounts for systematic risk
CAPM = RFR + [(MKT RTN - RFR) x Beta)]
Ex:
Assume that the return on the market is currently 10%, the 90 day Treasury bill rate of return is 4.5% and the beta coefficient of Stock X is 1.2.
What is the expected return on Stock X?
CAPM = RFR + [(MKT RTN- RFR) x Beta)]
.045 + [(.10 - .045)] x 1.2
.045 + (.055 x 1.2)
.045 + .066 =
.111 or 11.1%
.055 = mkt risk premium
.066 = stock risk premium
This is the amount of additional return the investor will need to invest (in excess of RFR) in specific stock and overall market.
Jensen’s Alpha
A measure of risk adjusted valued added by a portfolio manager.
(+) Alpha = portfolio mgr. added value
(-) Alpha = portfolio mgr. underperformed
Alpha = Avg Rtn of PfM- [RFR + (MKT RTN - RFR) x Beta)]
Ex:
Calculate Jensen’s Alpha to determine the extent to which Portfolio P outperformed or underperformed its CAPM benchmark.
Realized Portfolio Return: 10%
Portfolio P Beta: 0.50
Mkt. Portfolio mean Return: 12%
Risk Free Rate: 4%
Alpha = Avg Rtn of PfM- [RFR + (MKT RTN - RFR) x Beta)]
.10 - [0.04 + (.12 -.04) x .5] =
.10 - .08 =
0.02 or 2%
Treynor Ratio
Uses beta to compare the performance of diversified portfolios and stocks.
Treynor = Mkt Return - RFR ÷ Beta
Ex:
Portfolio RFR: 3%
Actual Mkt Return: 12%
Beta: .60
Treynor = .12 - .03 ÷ .60 = .15
*The higher the Treynor Ratio the better
*If Treynor ratio is higher than treynor of the mkt, then the portfolio manager has outperformed the market
Sharpe Ratio
This ratio is a relative measure of the risk-adjusted performance of a portfolio based on total risk (systematic and unsystematic risk)
Sharpe Ratio = Avg Rtn - RFR ÷ St. Deviation
Standard Deviation of a Two Asset Portfolio
Information Ratio
Measures the portfolios average rate of return in excess of a comparison benchmark divided by the st. deviation of the excess return.
IR = Fund Rtn - Benchmark Rtn ÷ Active risk
Ex:
Fund X return: 12%
Benchmark Return: 10%
Active Risk: 4%
12-10 ÷ 4 = .5
Constant Growth Dividend Discount Model
V = D1 ÷ r-g
V= Div @ yr1 ÷ req rate of rtn - div. grwth rt
Ex:
ABC stock is currently paying (year 0) a dividend of $2/share
The dividend will grow at a constant rate of 6% annually.
What should the stock be selling for in the investor’s required rate of return is 10%
V= $2 x (1 + .06) ÷ .10 - .06
V = $53
The investor should not pay more than $53 for the stock.
Bond Convexity
Duration is a useful tool to help investors determine the expected change in the price of a bond for changes in interest rates.
Convexity =
Duration X [chg. in int. rates ÷ 1 + Current YTM]
EX:
Mira’s portfolio includes a bond with the following characteristics:
Current Value $127,325
Average historical return 5%
Standard deviation 7%
Current YTM 5%
Duration 8 years
What would the new value be if interest rates increased to 6%?
Step 1:
Duration X [change in interest rates ÷ 1 + Current YTM]
-8.0 x [.0100 ÷ 1.05]
-8.0 x .0095 = -0.0760
Step 2:
Calculate change in bonds price X current value of bond
-0.0760 x 127325 = 9676.70
Step 3:
Subtract bond’s current value minus price movement
127325 – $9676.70 = $117,648.30 (new value of bond).
Call Option
A right to BUY a security for a specified price w/in specified timeframe
Buy a Call (being long)
Write a Call (being short)
Intrinsic Value: C-O-M-E
IV = mkt price - exercise price
EX 1:
FMV of stock: 30
Ex price: 40
IV = $0 (out of the $)
EX 2:
FMV of stock: 40
Ex price: 30
IV = $10 (in the $)
Time Value = premium - IV (intrinsic value)
Put Option
A right to SELL a security for a specified price w/in specified timeframe
Buy a PUT (being long)
Write a PUT (being short)
Intrinsic Value: P-O-E-M
IV = exercise price - mkt price
EX 1:
FMV of stock: 80
Ex price: 70
IV = 0 (out of the $)
EX 2:
FMV of stock: 70
Ex price: 80
IV = $10 (in the $)
Time Value = P-IV
Time Value = premium - IV (intrinsic value)
Geometric Mean
*will always been lower than arithmetic mean
Example:
Returns
15, 9, -6.5, 18, 16
End mode
1 P/Y
PV: -1
N: 5 (this is the total # of returns)
FV (1.15)(1.09)(.935)(1.18)(1.16)
Solve for I/YR: 9.9146
Effective Annual Return (EAR)
I. Annual percentage rate taking into consideration the impact of compounding
II. Provides the annual rate of interest of an investment or debt when compounding occurs more than once per year
PV: -1
N: 12
I/YR: 1.25 (15 ÷ 12)
Solve for FV: 1.608 (subtract 1 afterwards)
Holding Period Return
HRP = end value - bgn value +/- cash flows ÷ bgn value
Conversion Ratio
Is the stock price at which a convertible bond can be exchanged for shares of the issuer’s common stock
CR = par value of convertible security ÷ conversion price
EX:
Assume that a convertible bond has a conversion price of $40/share. If the par value of the bond is $1000. What is the conversion ratio
CR = 1000 ÷ 40
CR = 25
Margin Call
When the equity in an investor’s position drops below the maintenance margin percentage (min amount of cash held at broker dealer account)
margin call = debit balance ÷ 1 - maintenance margin
Ex:
Harry pays $20K to purchase ABC company currently trading at $25/share, using margin account.
Therefore $20K is also borrowed from the broker dealer. Harry can buy a total of 1600 shares.
At what point should Harry be concerned about receiving a margin call from the broker dealer?
MC = $25 x .5 ÷ 1 - 0.35
MC = 12.5 ÷ 0.65
MC = $19.23
Holding Period Return
Ralph bought 400 shares of LOA stock at $36 per share on margin (assume a 50% initial margin requirement). The margin interest was 7.5% annually. He sold the stock after one year for $49.50 per share. LOA did not pay any dividends during the holding period. What was Ralph’s holding period return using margin?
Answer: 67.50%
His HPR using margin was 67.50%, calculated as follows:
Ending value = 400 shares × $49.50 per share = $19,800
Beginning value = 400 shares × $36.00 per share = $14,400
Cash outflow = margin interest = 0.075 × 0.50 × $14,400 = $540
Initial investment = 0.50 × $14,400 = $7,200
HPR = ($19,800 − $14,400 − $540) ÷ $7,200 = 67.50%
Interest Rate Change in Bonds Price:
Lauren owns a AA rated corporate bond with a current market value of $987.34. The bond’s YTM changes from 5.45% to 4.98%. What is the estimated percent change in the price of the bond assuming a Macaulay duration of 4.6 years?
2.05%
Change in Price = -D x (new yield - old yield) ÷ (1 + old yield)
ΔP/P = −4.6 × [(0.0498 − 0.0545) ÷ (1 + 0.0545)]
Efficient Market Hypothesis (EMH)
“Technical analysis is not considered valid under the efficient market hypothesis because this type of analysis is attempting to predict future prices based on past price movement. Fundamental analysis allows investors to create portfolios that are consistent with their risk tolerances
Weak: Current stock prices already incorporated all historical market data & that historical prices trends are therefore of no value. People who think researching, studying, analyzing company will give them advantage in superior performance Fundamental analysis & insider info will yield superior performance.
People believe it may be possible to outperform the market by taking advantage of anomalies such as the small firm effect and the neglected firm effect.
Semi Strong: Current stock prices reflect all historical data & by analyzing financial data/industry/economic outlook…only insider info could produce above market returns all available information on the history of prices.
all publicly available information concerning a company. current stock prices not only reflect all historical price data, but also reflect data from analyzing financial statements, industry, or current economic outlook?
Strong: that current stock prices reflect all public and private information The morningstar enigma is NOT considered an anomaly to the EMH”
