Download Finance I - Universidade Nova de Lisboa

Finanças
October 26
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Topics covered

Returns





Dollar returns
Percentage returns
Holding period returns
Return statistics
Trade-off between risk and return
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Capital Market Theory

Previously, we have mostly focused on
risk-free cash flows discounted with

Most investment involve risky cash flows,
which need to be discounted with

The second part of this course focuses on
determining the discount rate for risky
cash flows.
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Returns

Income component for investment in
stocks

Example:



At t=0, you invest in a stock. You buy 100
shares of stock i at the price of P0=$37
At t=1, the stock pays dividends of $1.85 per
share.
The stock price P1=$40.33 or P1=$34.78.
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Returns

Dollar returns



Dividend income =
Capital gains =
or Capital losses =
Total dollar return
=
=
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Returns

Percentage returns: how much return do
we get for every dollar invested?

Dividend yield =

Capital gain =

Total return on investment
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Holding-period returns

The holding period return
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Holding-period returns

Suppose your investment provides the
following returns over a four-year
period:
Year Return Holding period return
1
10%
2
-5%
3
20%
4
15%
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Holding-period returns

A famous set of studies dealing with the rates of returns on
common stocks, bonds, and Treasury bills was conducted
by Roger Ibbotson and Rex Sinquefield.
Large-company common stocks:

Small-company common stocks:

Long-term corporate bonds:

Long-term U.S. government bonds:

U.S. treasury bills:

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The Future Value of an Investment
of $1 in 1925
$1,775.34
1000
$59.70
$17.48
10
Common Stocks
Long T-Bonds
T-Bills
0.1
1930
1940
1950
1960
1970
1980
1990
2000
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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Return statistics

average return

the standard deviation of those returns

the frequency distribution of the
returns.
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Historical Returns, 1926-2002
Series
Average
Annual Return
Standard
Deviation
Large Company Stocks
12.2%
20.5%
Small Company Stocks
16.9
33.2
Long-Term Corporate Bonds
6.2
8.7
Long-Term Government Bonds
5.8
9.4
U.S. Treasury Bills
3.8
3.2
Inflation
3.1
4.4
Distribution
– 90%
0%
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago
(annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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+ 90%
The Risk-Return Tradeoff
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Rates of Return 1926-2002
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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Stock return and risk-free return

Risk-free return:

Risk premium:
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Stock return and risk-free return

One of the most significant observations of stock
market data is this long-run excess of stock
return over the risk-free return.
Mean
Large company
12.2%
Small company
16.9%
Risk Premium Stan. Dev
Long-term corp bonds 6.2%
Long-term gov bonds
5.8%
U.S. treasury bills
3.8%
inflation
3.1%
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Risk statistics

Risk measured by the variance and
standard deviation of the return
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Normal Distribution

A large enough sample drawn from a normal
distribution looks like a bell-shaped curve.
Probability
– 3s
– 49.3%
– 2s
– 28.8%
– 1s
– 8.3%
0
12.2%
+ 1s
32.7%
+ 2s
53.2%
Return on
large company common
stocks
68.26%
95.44%
99.74%
+ 3s
73.7%
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