can have semiannual every 6 mnth period 2 pmt but compounded quarterly m4

# Can have semiannual every 6 mnth period 2 pmt but

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**can have semiannual (every 6 mnth, period =2) pmt but compounded quarterly (m=4) Annual Percentage Rate (APR) : Annual/ quoted i/r by law. APR = period rate x no. periods per year *If compounding period >1, EAR always > APR. Savers prefer monthly compound to yearly compound. EAR = APR when interest is compounded annually - PV of annuity falls as r rises; PV of annuity rises as r falls - FV of annuity rises as r rises; FV of annuity falls as r falls Implied disc rate *key in PV as (-), FV as positive No. Periods Loans 1. Pure discount loans No periodic interest payments. Principal and interest paid at maturity. Eg. T bill will sell for PV = FV/(1+r) 2. Interest only loans: Interest paid thru-out loan period; principal paid at maturity 3. Loans w fixed principal payments Eg. Corp bonds -Interest and fixed principal amt paid throughout the loan period -\$50,000 10 year loan at 8% i/r. Loan agreement req firm to pay 5k in principal each year + interest. Interest is first (0.08 x 5000), then (50,000 – 5k – 0.08x5000) (0.8) = 8600, then 8200, 7800, etc 4. Amortized loans: Loans and a portion of principal paid thru-out the loan period (Eg: Consider 4-year loan with annual payments, 8% i/r Principal Amt = \$5000) Ans: (Ordinary annuity) Find annual PMT = \$1509.06. PV=5000 cos bank give u today. Nx 4 yrs pay back constant instalment \$, not future lump sum (so FV = 0) W4: Risk & Return Actual/Expectd Returns historical/prospective, dollar/% terms Total Dollar Return (nominal) = Div income + capital gain/loss Dividend Yield (nominal) = Dividend/Initial Share Px Capital Gain Yield (nominal) = Capital Gain/Initial Share Px Total % Return (nominal) = Dividend Yield + Capital Gain Yield Inflation 1 + Real Rate of Return = (1 + nominal return)/(1+ inflation rate) Real Return (est) = Nominal Return – Expected Inflation Expected return - a stock r i = possible return (per diff econ situation) P i = probability of possible return Expected return - portfolio Method 1: weighted average of expected returns r i = possible return (per diff econ situation) w i = fraction of portfolio’s \$ value invested in stock i (or portfolio%), must add to 1 Method 2: sum [(return in scenario)(likelihood of scenario happening)] Arithmetic avg return/ arithmetic mean /Ex-post avg return/ Observed avg return/Historical avg return = r 1 + r 2 + …. + r n 1 + r n n What you earn in a typical year. If given px and dividends, use total % return to calculate return per year. Geometric avg return/ geometric mean /mean holding period return/avg compound return. What you actly earned per yr on average compounded annually) Holding period = n years r = actual nominal returns in year 1/2/etc Holding period return = ( 1 + r 1 ) ( 1 + r 2 ) ( .. ) ( 1 + r n 1 ) ( 1 + r n ) 1 Geometric avg return r g = ( 1 + r 1 ) ( 1 + r 2 ) ( .… ) ( 1 + r n 1 ) ( 1 + r n ) 1 Standard Deviation (Stock & Portfolio) Measures total risk or standalone risk of investment. ↑ Sd, ↑prob actual far frm expected returns. Standalone risk = risk if investor only held this 1 asset. r avg = avg annual return/arithmetic mean over last n years ˆ r : expected return r i = possible return Histo rical data n n i + 1 1 FV = i + 1 FV = PV n i i i P r r 1 ˆ n i i i p r w r 1 ˆ ˆ T r r T t t 1 1 1 2 n r r n t Avg t i n i i P r r 2 1 ˆ 2 Variance

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• Winter '14