CH 5: Risk and Return: Past and rologue

Question 1

What is Holding Period Return?

Answer 1

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

Question 2

ways to find the Rate of Return of multiple periods with inflows and outflows.

Answer 2

1. Arithmetic mean
2. Geometric mean (time-weighted)
3. Dollar weighted return (IRR)

Question 3

How to find the Arithmetic mean and the Geometric mean?

Answer 3

Ra = [Sum (Yearly_RoR)] / n

Rg = [product (1 + Yearly_RoR) ]^ (1/n) - 1

Question 4

What is IRR and how to find it?

Answer 4

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.

Question 5

What is the problem with arithmetic mean?

Answer 5

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.

Question 6

What is the formula for IRR for one period?

Answer 6

FV = PV (1 + IRR)^n

IRR = (PV /FV)^(1/n) - 1

Question 7

What is the effective Annual Rate (EAR)?

Answer 7

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 *

Question 8

(under Discrete Probability Distribution) Find the expected value E(r) (weighted mean).

Answer 8

= Sum( p(s) * r(s))

P- Probability a state occurs
r - return if a state occurs

Question 9

Standard Deviation

Answer 9

Variance (sd)^2 = Sum( p(s) [r - weighted_mean]^2)

Standard Deviation = sqroot(variance)

Question 10

If the data is historical, then

Answer 10

you dont need to use the weighted average method.

Question 11

What is the EAR, if compounding is continues

Answer 11

EAR = e^APR - 1

Question 12

what is APR ?

Answer 12

annualized rate.

APR = periodic_rate * m

Question 13

Two main approaches to measuring risk are:

Answer 13

1. Using historical data
2. Using probabilities
   a. Continuous probability distribution.
   b. Discrete probability distribution.

Question 14

Historical statistics

Answer 14

E(r) = r bar = Sum(r) / n

Variance = Sum(r - rbar)^2 / (n - 1)

standard deviation is Sx on calc = sqroot(Variance)

Question 15

List the Distribution b/w the Sd, in a standard normal deviation.

Answer 15

68. 26%: b/w +-1 SD
69. 44: b/w +-2SD
70. 74: b/w +-3SD

Question 16

Find the standardized return (z-score)

Answer 16

sr = (r - E(r)) / SD

Question 17

Stocks follow a normal distribution over a short period of time.

Answer 17

True

Question 18

Value at risk answer what questions?

Answer 18

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?

Question 19

the typical probability used is 5%. what HPR and what dollar loss corresponds to a 5% probability?

Answer 19

from sr = (r - E(r)) / SD
(Basically Normal inverse function)
r = E(r) + sr*SD
at 5%

r = E(r) + -1.64485*SD

Question 20

What is:

1. Interest rate*
2. nominal rate
3. real rate
4. Real risk-free rate

Answer 20

1. % return earned by a lender and paid by a borrower. Price of money per unit of time
2. Stated rate on a specific debt security. not adjusted to inflation
3. Net % increase in wealth or purchasing power from an investment .
4. the net % increase in wealth that would be expected from investing in a security that was free of risk.

Question 21

Fisher Rule (and show how you found it for real rate)

Answer 21

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

Question 22

Risk Control ways:

Answer 22

asset allocation

efficient diversification

Question 23

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%?

Answer 23

“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

Question 24

What is asset allocation?

and list the abbreviation of its components.

Answer 24

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

Question 25

What is the ROR (and Expected ROR) on a portfolio? Write the equation and modify it to a linear function.

Answer 25

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

Question 26

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!

Answer 26

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