Efective Annual Rate EAR
Actual rate after taking into consideration any
compounding that may occur during the year.
Need to ensure that interest rate and time period
matches
1
+
APR
m
¿
¿
EAR
=
¿
Implied Discount Rate
i
=(
FV
PV
)
1
/
n
−
1
For # of periods,
1
+
r
t
=
ln
(
FV
PV
)/
ln
¿¿
Diferent types of loans
1) Pure Discount Loans: Payment of principal and
interest rate at maturity
2) Interest only Loans: Interest paid annually but
principal at maturity
3) Loan with fixed principal payment: Fixed principal
portion and interest varies throughout loan period
4) Amortised Loan: Equal payment per period, include
principal+interest
Chapter 4 and 5: Risk and Return
Diferent types of portfolios:S&P 500(Standard and
Poor), Small stocks, World Portfolio, Corporate Bonds,
Treasury Bills
•
Investment returns
measure the financial results of an
investment.
•
Returns may be
historical
or
prospective
Dollar terms:
Amount received – Amount invested
Percentage terms:
Amount received – Amount invested
Amount invested
Totaldollar return
=
¿
income
+
Capital ga
Percentage Return
: Dividend yield and capital gain yield
Dividend yield
=
Dividend
InitialSHare Price
Capital gain yield
=
CapitalGain
Initial share price
The impact of inflation: Real VS Nominal
Nominal return: Actual $ received versus actual $ given
up
Real rate of return
:
How much
more
you will be able to
buy with your money at the end of the year. Taken
inflation into account.
Fisher Equation: Convert nominal rate to real rate
1
+
r
=
1
+
N
1
+
: OR Common approximation
Realreturn
=
Nomialreturn
−
Expected infla
Expected Returns
^
r
=
∑
i
=
1
n
r
i
p
i
Arithmetic Average Return
´
r
=
∑
t
=
1
T
r
t
T
Risk
: The uncertainty associated with future possible
outcomes
Measure variability in investment returns via the
Standard Deviation
o
=
√
∑
i
=
1
n
(
r
i
−
^
r
)
P
i
SD measures total risk,
larger SD, high probability that actual returns far from
expected. SD measures dispersion around expected
value.
Stand-Alone Risk: Risk an investor would face if he only
held one asset.
Using historical data to estimate the SD
Estimated o
=
√
∑
t
=
1
n
(
r
t
−
r
avg
)
2
n
−
1
Coeficient
of Variation:
Standardized measure of dispersion about
the expected value, that shows the risk per unit of
return.
CV
=
Standard Deviation
Expeted rateof return
CV
=
Standard Deviation
Mean
Lower CV indicates less relative variability or lower risk
per unit
Risk, return and Financial Markets
• Greater the potential reward, greater the risk Risk-
return trade of
• Low risk, low potential returns. High risk, high
potential returns
• Financial markets allow companies, govt and
individuals to increase utility by matching borrower
(Better access to capital to invest in productive assets)
to savers (Ability to invest in financial assets)
• Risk Aversion: Assumes investors dislike risk and
require higher rates of return to encourage them to hold
riskier securities
• Risk Premium: Return over and above the risk-free
rate
• Risk free rate is the long term government bond rate
r=Possible return
p=Probability of

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- Spring '11
- tohmunheng
- Investing