Download presentation

Published byCharles Tyler Modified over 7 years ago

1

Risk and Return Holding Period Return Multi-period Return

Return Distribution Historical Record Risk and Return

2

Single Period Return Holding Period Return: Example

Percentage gain during a period HPR: holding period return P0: beginning price P1: ending price D1: cash dividend Example You bought a stock at $20. A year later, the stock price appreciates to $24. You also receive a cash dividend of $1 during the year. What’s the HPR? P0 P1+D1 t = 0 t = 1 Investments 7

3

Multi-period Return What’s the return over a few periods?

Consider a mutual fund story Net inflow when the fund does well Net outflow when the fund does poorly Question: How would we characterize the fund’s performance over the year? Investments 7

4

Multi-period Return Arithmetic Average

Sum of each period return scaled by the number of periods ra: arithmetic return ri: HPR in the ith period N: number of periods Example: Calculate the arithmetic return of the fund Investments 7

5

Multi-period Return Geometric Average

Investments 7 Multi-period Return Geometric Average Single period return giving the same cumulative performance as the sequence of actual returns rg: geometric return ri: HPR in the ith period N: number of periods Example: Calculate the geometric return of the fund Investments 7

6

Multi-period Return: Dollar-weighted

Internal Rate of Return (IRR) The discount rate that sets the present value of the future cash flows equal to the amount of initial investment Considers change in the initial investment Conventions (from investor’s viewpoint) Initial investment as outflow (negative) Ending value as inflow (positive) Additional investment as outflow (negative) Reduced investment as inflow (positive) Investments 7

7

Multi-period Return: Dollar-weighted

Example: IRR = ? (assets in million dollars) By definition Using Excel t =0 t =1 t =2 t =3 t =4 CF0 = -1 CF1 = -.1 CF2 = -.5 CF3 = .8 CF4 = 1.0 Investments 7

8

Multi-period Return: APR vs. EAR

APR – arithmetic average EAR – geometric average T: length of a holding period (in years) HPR: holding period return APR and EAR relationship Investments 7

9

Multi-period Return – Examples

25-year zero-coupon Treasury Bond Example 2 What’s the APR and EAR if monthly return is 1% Investments 7

10

Return (Probability) Distribution

Moments of probability distribution Mean: measure of central tendency Variance or Standard Deviation (SD): measure of dispersion – measures RISK Median: measure of half population point Return Distribution Describe frequency of returns falling to different levels Investments 7

11

Risk and Return Measures

You decide to invest in IBM, what will be your return over next year? Scenario Analysis vs. Historical Record Scenario Analysis: Investments 7

12

Risk and Return Measures

Scenario Analysis and Probability Distribution Expected Return Return Variance Standard Deviation (“Risk”) Investments 7

13

Risk and Return Measures

More Numerical Analysis Using Excel Investments 7

14

Risk and Return Measures

Example Current stock price $23.50. Forecast by analysts: optimistic analysts (7): $35 target and $4.4 dividend neutral analysts (6): $27 target and $4 dividend pessimistic analysts (7): $15 target and $4 dividend Expected HPR? Standard Deviation? Investments 7

15

Historical Record Annual HPR of different securities

Risk premium = asset return – risk free return Real return = nominal return – inflation From historical record Risk Premium and Real Return are based on APR, i.e. arithmetic average Investments 7

16

Real vs. Nominal Rate Real vs. Nominal Rate – Exact Calculation:

R: nominal interest rate (in monetary terms) r: real interest rate (in purchasing powers) i: inflation rate Approximation (low inflation): Example 8% nominal rate, 5% inflation, real rate? Exact: Approximation: Investments 7

17

Risk and Horizon S&P 500 Returns 1970 – 2005 How do they compare* ?

Mean *260 = 8.866% Std. Dev *260 = % SURPRISED??? Daily Yearly Mean 0.0341% 8.9526% Std. Dev. 1.0001% % * There is approximately 260 working days in a year Investments 7

18

It is accepted that stock returns are independent across time

Consecutive Returns It is accepted that stock returns are independent across time Consider 260 days of returns r1,…, r260 Means: E(ryear) = E(r1) + … + E(r260) Variances vs. Standard Deviations: s(ryear) ¹ s(r1) + … + s(r260) Var(ryear) = Var(r1) + … + Var(r260) Investments 7

19

Consecutive Returns Volatility

Daily volatility seems to be disproportionately huge! S&P 500 Calculations Daily: Var(rday) = ^2 = Yearly: Var(ryear) = *260 = Yearly: Bottom line: Short-term risks are big, but they “cancel out” in the long run! Investments 7

20

Accounting for Risk – Sharpe Ratio

Reward-to-Variability (Sharpe) Ratio E[r] – rf – Risk Premium r – rf Excess Return Sharpe ratio for a portfolio: or Investments 7

21

Wrap-up What is the holding period return?

What are the major ways of calculating multi-period returns? What are the important moments of a probability distribution? How do we measure risk and return? Investments 7

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.