CH 5: Risk and Return: Past and rologue Flashcards
What is Holding Period Return?
HPR = [(P1 - P0) +D1] / P0
Also HPR = [“Dividend_Yield” (D1/P0)] + [“Capital_Gains_Yield ((P1 -P0) / P0)]
P0: Beg. Price
P1: Ending Price
D1: Cash Dividends
ways to find the Rate of Return of multiple periods with inflows and outflows.
- Arithmetic mean
- Geometric mean (time-weighted)
- Dollar weighted return (IRR)
How to find the Arithmetic mean and the Geometric mean?
Ra = [Sum (Yearly_RoR)] / n
Rg = [product (1 + Yearly_RoR) ]^ (1/n) - 1
What is IRR and how to find it?
the IRR is a discount Rate that equates the present value of the future cash flows to the initial outlay.
We find it with trial and error.
What is the problem with arithmetic mean?
It over states the historical RR (over many periods). The geometric mean solve that.
but if we want a prediction then the arithmetic mean would be appropriate.
What is the formula for IRR for one period?
FV = PV (1 + IRR)^n
IRR = (PV /FV)^(1/n) - 1
What is the effective Annual Rate (EAR)?
The rate of interest actually earned. It considers compounding.
EAR = Amount_of_compounded_interest_over_year / Amount_invested_in_one_Year
EAR = [(1 + APR/m)^m] -1
m: compounding periods
* on the calc use: conversion *
(under Discrete Probability Distribution) Find the expected value E(r) (weighted mean).
= Sum( p(s) * r(s))
P- Probability a state occurs
r - return if a state occurs
Standard Deviation
Variance (sd)^2 = Sum( p(s) [r - weighted_mean]^2)
Standard Deviation = sqroot(variance)
If the data is historical, then
you dont need to use the weighted average method.
What is the EAR, if compounding is continues
EAR = e^APR - 1
what is APR ?
annualized rate.
APR = periodic_rate * m
Two main approaches to measuring risk are:
- Using historical data
- Using probabilities
a. Continuous probability distribution.
b. Discrete probability distribution.
Historical statistics
E(r) = r bar = Sum(r) / n
Variance = Sum(r - rbar)^2 / (n - 1)
standard deviation is Sx on calc = sqroot(Variance)
List the Distribution b/w the Sd, in a standard normal deviation.
- 26%: b/w +-1 SD
- 44: b/w +-2SD
- 74: b/w +-3SD
Find the standardized return (z-score)
sr = (r - E(r)) / SD
Stocks follow a normal distribution over a short period of time.
True
Value at risk answer what questions?
what is the greatest amount I can expect to lose on my portfolio in a given rime period at a given level of prob.
the typical probability used is 5%. what HPR and what dollar loss corresponds to a 5% probability?
the typical probability used is 5%. what HPR and what dollar loss corresponds to a 5% probability?
from sr = (r - E(r)) / SD
(Basically Normal inverse function)
r = E(r) + sr*SD
at 5%
r = E(r) + -1.64485*SD
What is:
- Interest rate*
- nominal rate
- real rate
- Real risk-free rate
- % return earned by a lender and paid by a borrower. Price of money per unit of time
- Stated rate on a specific debt security. not adjusted to inflation
- Net % increase in wealth or purchasing power from an investment .
- the net % increase in wealth that would be expected from investing in a security that was free of risk.
Fisher Rule (and show how you found it for real rate)
1 + R = (1 + r) (1 + i)
R = 1 + r + i +ri - 1 R = r + i +ri R = i + r(1 + i) r = (R - i) / (1 +i)
1 + R = (1 +r) / (1+i)
R: Nominal
r: real
i: inflation
Risk Control ways:
asset allocation
efficient diversification
HW Q5: What is your estimate of the expected annual HPR on the S&P 500 stock portfolio if the current risk-free interest rate is 4.4%?
“Large Stocks” is the standards and poor’s market value-weighted portfolio of 500 US common stocks.
Therefore, Estimated HPR = Return_in_excess_of_1month_Tbill_rate + Risk_free_rate
What is asset allocation?
and list the abbreviation of its components.
A strategy to control portfolio risk by specidying the fraction of portfolio invested in classes such as stocks, bonds,and risk-free assets.
C - The complete portfolio
F - The Risk Free asset
P - Risky portifolio
y - % of C (the investment budget) allocated to F (Risky portfolio)
(1 - y) - % of C allocated to
——————-
wi - Weight of individual asset i in P
wi* - Weight of individual asset i in C (the whole thing)
——————
rp - ROR to P
rf = E(rf) - ROR to F
SDp - Standard deviation of rp
SDf - Standard deviation of rf (which is 0)
corr - correlation
What is the ROR (and Expected ROR) on a portfolio? Write the equation and modify it to a linear function.
it is the weighted average of component security returns, with the investment proportions as weights.
rc = y.rp + (1 - y).rf
E(rc) = y.E(rp) + (1 - y).rf
…
E(rc) = y.(E(rp) - rf) + rf
Is the SD of a portfolio equal to the weighted average of the components SDs? and why so?
Write down the equation for SDp (with 2 assets) and the SDc!
No it is not. That is because all the components are not 100% positively correlated.
Variance
SDp^2 = (w1.SD1)^2 + (w2.SD2)^2 + 2(w1.SD1)(w2.SD2).(Corr1,2)
SDc = y.SDp
