A random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing


Illustration: Expected Return and



Download 5,3 Mb.
Pdf ko'rish
bet92/212
Sana26.02.2022
Hajmi5,3 Mb.
#467845
1   ...   88   89   90   91   92   93   94   95   ...   212
Bog'liq
A Random Walk Down Wall Street The Time

Illustration: Expected Return and
Variance Measures of Reward and
Risk


This simple example will illustrate the concept of expected
return and variance and how these are measured. Suppose
you buy a stock from which you expect the following overall
returns (including both dividends and price changes) under
different economic conditions:
Business Conditions
Possibility of
Occurrence
Expected
Return
“Normal” economic
conditions
1 chance in 3
10%
Rapid real growth without
inflation
1 chance in 3
30%
Recession with inflation
(stagflation)
1 chance in 3
–10%
If, on average, a third of past years have been “normal,”
another third characterized by rapid growth without inflation,
and the remaining third characterized by “stagflation,” it
might be reasonable to take these relative frequencies of past


events and treat them as our best guesses (probabilities) of
the likelihood of future business conditions. We could then
say that an investor’s expected return is 10 percent. One-
third of the time the investor gets 30 percent, another one-
third 10 percent, and the rest of the time she suffers a 10
percent loss. This means that, on average, her yearly return
will turn out to be 10 percent.
Expected return = 
1
/
3
(0.30) + 
1
/
3
(0.10) + 
1
/
3
(–0.10) = 0.10.
The yearly returns will be quite variable, however, ranging
from a 30 percent gain to a 10 percent loss. The “variance” is
a measure of the dispersion of returns. It is defined as the
average squared deviation of each possible return from its
average (or expected) value, which we just saw was 10
percent.
Variance = 
1
/
3
(0.30–0.10)
2

1
/
3
(0.10–0.10)
2

1
/
3
(–0.10–
0.10)
2



1
/
3
(0.20)
2
+ 1/3(0.00)
2

1
/
3
(–0.20)
2
= 0.0267.
The square root of the variance is known as the standard
deviation. In this example, the standard deviation equals
0.1634.
Dispersion measures of risk such as variance and standard
deviation have failed to satisfy everyone. “Surely riskiness is
not related to variance itself,” the critics say. “If the
dispersion results from happy surprises—that is, from
outcomes turning out better than expected—no investors in
their right minds would call that risk.”
It is, of course, quite true that only the possibility of
downward disappointments constitutes risk. Nevertheless, as
a practical matter, as long as the distribution of returns is
symmetric—that is, as long as the chances of extraordinary
gain are roughly the same as the probabilities for
disappointing returns and losses—a dispersion or variance
measure will suffice as a risk measure. The greater the
dispersion or variance, the greater the possibilities for
disappointment.
Although the pattern of historical returns from individual


securities has not usually been symmetric, the returns from
well-diversified portfolios of stocks are at least roughly
symmetrical. The following chart shows the distribution of
monthly security returns for a portfolio invested in the S&P
500-Stock Index over seventy years. It was constructed by
dividing the range of returns into equal intervals (of
approximately 1¼ percent) and then noting the frequency
(the number of months) with which the returns fell within
each interval. On average, the portfolio returned close to 1
percent per month or about 11 percent per year. In periods
when the market declined sharply, however, the portfolio
also plunged, losing more than 20 percent in a single month.

Download 5,3 Mb.

Do'stlaringiz bilan baham:
1   ...   88   89   90   91   92   93   94   95   ...   212




Ma'lumotlar bazasi mualliflik huquqi bilan himoyalangan ©hozir.org 2024
ma'muriyatiga murojaat qiling

kiriting | ro'yxatdan o'tish
    Bosh sahifa
юртда тантана
Боғда битган
Бугун юртда
Эшитганлар жилманглар
Эшитмадим деманглар
битган бодомлар
Yangiariq tumani
qitish marakazi
Raqamli texnologiyalar
ilishida muhokamadan
tasdiqqa tavsiya
tavsiya etilgan
iqtisodiyot kafedrasi
steiermarkischen landesregierung
asarlaringizni yuboring
o'zingizning asarlaringizni
Iltimos faqat
faqat o'zingizning
steierm rkischen
landesregierung fachabteilung
rkischen landesregierung
hamshira loyihasi
loyihasi mavsum
faolyatining oqibatlari
asosiy adabiyotlar
fakulteti ahborot
ahborot havfsizligi
havfsizligi kafedrasi
fanidan bo’yicha
fakulteti iqtisodiyot
boshqaruv fakulteti
chiqarishda boshqaruv
ishlab chiqarishda
iqtisodiyot fakultet
multiservis tarmoqlari
fanidan asosiy
Uzbek fanidan
mavzulari potok
asosidagi multiservis
'aliyyil a'ziym
billahil 'aliyyil
illaa billahil
quvvata illaa
falah' deganida
Kompyuter savodxonligi
bo’yicha mustaqil
'alal falah'
Hayya 'alal
'alas soloh
Hayya 'alas
mavsum boyicha


yuklab olish