**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
- Capital Asset Pricing Model, Investing