Investment Analysis Bus350 Return and Risk Calculation

• Professor Tao Wang • Tel: x5445 • E-mail: [email protected]

• Room: PH154 • Office Hour: W, F 12:15pm – 1:15pm • Coursepage: http://www.qc.edu/~twang/course/350/i nvestments.html

the webpage.

. Announcements, homework, cases, exam dates are all on

Course Overview • Book: Investment Analysis and Portfolio Management by Reilly and Brown • CFA-designated Textbook • Group case (10%), three homework (5%), two midterms (50%) and one final (30%). Class participation is 5%.

Contents • Calculate return and risk based on distribution for a single asset • Calculate return and risk for a portfolio of assets • Holding Period Return • Real life indices • Calculate return and risk from index example, geometric mean and arithmetic mean comparison

Probability Distributions of Returns • Assume that there are two stock available, GENCO and RISCO, and each responds to the state of the economy according to the following table

Returns on GENCO & RISCO State of Economy Strong Return on RISCO 50% Return on GENCO 30% Prob ability 0.20

Normal 10% 10% 0.60

Weak -30% -10% 0.20

•

Probability Distributions of Returns of GENCO and RISCO

•0.6

•0.5

•0.4

•

Probability

•0.3

•0.2

•0.1

•0 •50% •30% •

Return

•10% •-10% •-30% •GENCO •RISCO

Observation • Both companies have the same expected return, but there is considerably more risk associated with RISCO

Equations: Mean 

r



E



P



r



P

1

r

1 

P

2

r

2 

P

3

r

3  ...

P n r n



r GENCO



r GENCO

 

i n

  1

P i r i

0 .

2  0 .

3  0 .

6  0 .

10  0 .

2  (  0 .

10 )  0 .

10  10 % Also : 

r RISCO

 10 %

Equations: Standard Deviation 

r

 

E

 

r



E

   2 

P

1 

r

1  

r

 2 

P

2 

r

2  

r

 2  ...



P n



r n

 

r

 2  

r GENCO



r GENCO

 

i n

  1

P i



r i

 

r

 2 0 .

2  Also : 

r RISCO

 0 .

2530  0 .

30  0 .

10  2 0 .

016  0 .

1265  0 .

6   0 .

10  0 .

10  2  0 .

2  (  0 .

10  0 .

10 ) 2

Observation • The expected returns of GENCO and RISCO happen to be equal, but the volatility, or standard deviation, of RISCO is twice that of GENCO’s • Which stock would a typical investor prefer

Example 1. Calculate the expected return and standard deviation of the following stock A: State 1 2 Probability 20% 60% Return 15% 10% 3 20% -8% The mean is 0.2*0.15+0.6*0.1+0.2*(-0.08) = 7.4% The standard deviation is: S.D. = Sqrt[0.2*(0.15-0.074)^2+0.6*(0.1 0.074)^2+0.2*(-0.08-0.074)^2] = 7.9%

Portfolio Return and Risk • Suppose you invest in two assets: stocks and bonds.

• Stocks offer a return of 10% with standard deviation of 15% • Bonds offer a return of 6% with standard deviation of 8%

Portfolio weight • If the investment weight on stocks is 50%, on bonds is 50%, what’s the return on the portfolio?

• What about the risk of the portfolio?

Holding Period Return HPR  Ending Price Beginning Price  Beginning $220  200  10  0 .

15 $200 Price  Dividend

Measures of Historical Rates of Return

Arithmetic AM   Mean HPR/

n

: where :  HPR  the sum of annual holding period yields

Measures of Historical Rates of Return • Geometric Mean GM    (1  HPR)  1

n

 1 where :   the product of the annual holding period returns as follows :  1  HPR 1   1  HPR 2   1  HPR

n



• Arithmetic mean is used for forecasting future returns • Geometric mean is used to calculate real past returns • Geometric mean has upward bias

Measure volatility • Historical volatility – Standard deviation – Realized volatility • Future volatility

Stylized facts • Stock/Bond returns are fairly difficult to predict • But return volatilities are predictable to a degree

Yahoo finance • Most indices historical data can be downloaded from http://finance.yahoo.com