Economics 434

Professor BurtonFall 2015

September 1, 2015

Public Stock

• Main subject of this course

• Anonymous purchase and sale using a broker-dealer registered with SEC

Return has two main components

August 28, 2014

Capital Gain

• Increase in stock value

• Pt+1 - Pt

Dividend

• Cash payments• Usually every 3

months• Dt

Where P is price, t is time, D is dividend at time t

Calculating the Rate of Return for a stock

1. First determine the time period (t)2. Then calculate the capital gain or loss ()3. Total the dividends received during the period ()

• Usually paid on a quarterly basis• Some stocks do not pay dividends (e.g. technology stocks)

4. If today is time t, then the above can be calculated (since , , and are all known)

September 1, 2015

Rate of Return during period (t-1, t) =

Where D is total dividends received during the period from t-1 to t

September 1, 2015

1928

1929

1930

1931

1932

1933

1934

1935

1936

1937

1938

1939

1940

1941

1942

1943

1944

1945

1946

1947

1948

1949

1950

1951

1952

1953

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

-60.00%

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%Yearly Stock Returns - 1928 to 2013

• Over the past 100 years, the average stock has returned approximately 10 percent per year

• Considerable volatility(variance) involved with this return

• 10 percent is an extraordinarily high number; larger than one would expect

• But, it is what it is!

• Calculating returns for today is fine and all, but what we really want to know is the stock’s return in the next period (t+1)

• But we can only guess since all we know today is Pt

September 1, 2015

Rate of Return during period (t, t+1) =

Asset choice in a two period economy

• Suppose that the world only has two periods; there is only one more period after today

• Suppose we want to buy assets now (in this period) that will do well by the end of this upcoming single period

• What should we own?

September 1, 2015

Possible states in a two period economy

• What can happen?

• We can simplify and just think about these three possibilities

September 1, 2015

Now S2

S1

S3

State 1 – Gets better

State 2 – Gets worse

State 3 – Muddles along

Economy

Three possible states and three available assets

• Three states can occur – Good, bad, and mediocre (S1, S2, S3)

• What are the available assets? X1, X2, X3

• How will each asset perform in each state?

September 1, 2015

The Definition of a “Real-World” Security

• Given the states of the world: s1, s2, s3• A security is defined by its payoff in dollars in

each state of the world– pi, 1 is the payoff for security i in state one

– pi, 2 is the payoff for security i in state two

– pi, 3 is the payoff for security i in state three

September 1, 2015

s1

s3

s2

Definition of Securities

X1 X2 X3 X4 X5

P1,1

P1,2P1,2

P1,1

P1,3

P2,1

P2,2

P2,3

P3,1

P3,2

P3,3

P4,1P5,1

P4,2 P5,2

P4,3 P5,3

September 1, 2015

What would constitute a riskless asset?

• A riskless asset returns the exact same amount in each state– Might be negative (a riskless asset can have a negative

return), but this loss is known in advance– Return has to be same in each state to have no risk– If there is more than one riskless asset, “the” riskless asset

used will be the one with the highest return

September 1, 2015

What would constitute a riskless asset?

• Assume that owning one unit of X1 will return exactly 1 dollar regardless of state– Return doesn’t have to be 1; could be anything. Easier to

simply assume 1 unit of return in each state

• X1 is the “riskless asset”

September 1, 2015

X1 $1

$1

$1

State 1 – Economy gets better

State 2 – Economy gets worse

State 3 – Economy muddles along

Return

September 1, 2015