Investments - Lect. 4-6 Flashcards
What 4 functions are performed by investment companies?
1) Record keeping and administration, (2) Diversification and divisibility, (3) Professional management, and (4) Lower transaction costs
NAV stands for:
Net Asset Value
Formula to calculate NAV:
(Market Value of Assets - Liabilities) / Shares Outstanding
Open End funds vs. Close End funds - Buy back
Open-end funds buy back shares at NAV. Close-end funds have set # of shares outstanding, if investors want to sell they have to sell to another customer/investor
Open End funds vs. Close End funds - Sell Price
Open-end funds sell at NAV or above IF it has a load/sales commission. Close-edn funds sell at premium at issuance then a discount as it ages.
Key points of a Hedge Fund:
1) Structures as private partnership = not subject to many SEC regulations (2) May require investors to agree to “lock-ups” - Periods where funds can’t be withdrawn (3) Pursues strategies mutual funds can’t - derivatives and short sales.
Cost of investing in Mutual Funds: Commission or sales charge when you first purchase
shares (not exceed 8.5%, normally lower than 6%)
Front-End Load
Cost of investing in Mutual Funds: Exit fee when you sell your shares (typically 5%-6%, decrease by 1% each year)
Back-End Load
Cost of investing in Mutual Funds: Funds allow use of fund assets to pay for distribution costs. Similar to operating expenses, deducted from assets, but capped at 1% average net assets per year
12b-1 Charges
Rate of return on mutual fund formula:
(EndNAV - BegNAV + Div + CapGain) / BegNAV
Taxation of mutual funds:
1) “Pass-through status,” funds not taxed, investors taxed on income from fund (2) Can’t decide when to realize cap gains and losses for tax benefits (3) MFs with high turnover are tax inefficient
Exchange-Traded Funds vs. Mutual Funds - Pricing/Trading
ETFs trade shares continuously, MFs priced once per day
Exchange Traded Funds Advantages over Mutual Funds:
1) Can be traded continuously during the day (2) Tax advantage over mutual funds (3) Funds cannot depart from NAV for long periods (4) Cheaper than mutual funds
Disadvantages to Mutual Funds:
1) Must purchase from broker for a fee and includes bid-ask spread (2) can depart from NAV for short periods in ways that overwhelm cost advantages to ETFs
Type of risk that can be eliminated through diversification:
Idiosyncratic, Nonsystematic, or Diversifiable
Type of risk that can’t be eliminated through diversification:
Systematic, Market or Nondiversifiable
Correlation between bond and stock funds
Negatively correlated
Formula: Portfolio Variance
= (Wb x SDb)^2 + (Ws x SDs)^2 + 2(Wb x SDb) x (Ws x SDs) x Correlation Coefficient(bs)
Portfolio A will dominate Portfolio B as long as:
ExpRetA >= ExpRetB AND
SDa <= SDb
Formula: Sharpe Ratio
(E(Rp) - RF) / SDp
How to determine which portfolio will be optimal?
Highest Sharpe Ratio
Positive Alpha indicates:
Security is undervalued
Formula: Variance of Excess return
(Beta^2 x SDmrkt^2) + SD(ei-FirmSpec)^2
Formula: Alpha
Rs - (Beta(s) x Rmkt)
Formula: Ws0
(AlphaS / SD(S)^2) / (Rmkt / SDmkt^2)
Formula: Weight using beta
Ws0 / (1 + Ws0 x (1 - BetaS))
Formula: Sharpe Ratio of Portfolio
(AlphaA / SdA)^2
Strategy: Invest everything in risky portfolio each year
“Two-In” Strategy
Strategy: Invest in risk-free asset in year 1, risky portfolio in year 2
“One-In” Strategy
Strategy: Invest half in risky portfolio and half in risk free each year
“Half-in-Two” Strategy
Formula: HPR = Holding Period Return
(EndP - BegP + Div) / BegP
Problem with arithmetic average of returns:
Ignores compounding
Formula: Geometric Average
HPR %’s: if positive +1, if negative 1 - % - Example: 10, 25, -20, 20 = (1.10 x 1.25 x .80 x 1.20) ^(1/4) -1
Dollar weighted average return =
internal rate of return (IRR)
APR vs. EAR
Annual Percentage Rate ignores compounding interest while Effective Annual Rate includes compounding interest
If returns are normally distributed then:
1) Portfolio with returns normally distributed will have returns that are too (2) Completely described by mean and SD (3) SD is the measure of risk foe a portfolio of assets w/normally distributed returns
Formula: VaR Value at Risk
VaR = E(r) + (-1.64485)SD
Difference between speculation and gambling:
Risk Premia
Formula: Degree of Risk Aversion
( E(Rq) - Rf ) / Sdq^2
Formula: Real Interest Rate
Nominal Interest Rate - Inflation
Determining the fraction of a portfolio to be invested in broad asset classes such as stocks, bonds, or Treasury bills:
Asset Allocation
Focusing on choosing the percentage of risky versus risk-free assets in the portfolio:
Capital Allocation
Money market instruments are effectively risk-free due to:
Immunity to interest rate risk
Formula: Where on capital allocation line, given degree of risk aversion:
[ E(Rp) - Rf ] / [A x SDp^2)