Download Unito Corso di finanza e mercati finanziari internazionali

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
Corso di finanza e mercati
finanziari internazionali
I rischi finanziari
Prof. Vittorio de Pedys, ESCP
Europe, Unito
Il rischio (1/2)
σi
=> Rischio
Rappresenta la possibilità di realizzare un rendimento diverso da quello
atteso.
Misura del grado di dispersione della distribuzione di una variabile casuale (il
rendimento in questo caso) dal suo valore atteso.
Il rischio (2/2)
•VOLATILITA’ DEI RENDIMENTI = variabilità nel tempo
•Si calcola come SCARTO QUADRATICO MEDIO
r

 Ri
Rmi
= rendimenti singolo periodo
Rm
= rendimento medio atteso
 Rm
N
2
Rischio specifico e rischio sistematico
La figura dimostra che con la diversificazione si può ridurre (fino ad
annullarlo) il rischio specifico, ma non quello sistematico
Rischio di Mercato Vs. rischio specifico
Rischio totale
Rischio specifico
(unico, residuo, diversificabile)
Rischio sistematico
(rischio di mercato)
Riguarda una particolare azienda e può
essere ridotto dalla diversificazione
– un competitor brevetta una nuova
tecnologia
– I sindacati vanno in sciopero in uno
stabilimento produttivo
– Un forte competitor entra nel settore
Riguarda tutte le aziende e non può essere
ridotto dalla diversificazione
– L’inflazione cresce inaspettatamente
– Instabilità politica, guerre…
– Federal Reserve alza I tassi di interesse
– Il ciclo economico o industriale cambia
Il rischio specifico deve essere riflesso
nei flussi di cassa previsionali, non nel
rasso di sconto
Il rischio di mercato deve essere riflesso
nel flussi di cassa e nel costo del capitale.
Non può essere diversificato e gli
investitori vogliono essere compensati
per supportarlo
Rischio e rendimento
• Diversificando il portafoglio su diversi businesses,
gli investitori possono eliminare il rischio specifico
associato a ciascun singolo investimento. Il riscio di
Mercato non può essere eliminato.
Variability
Variance
Specific
Risk
Market Risk
Number of Securities
USING STANDARD DEVIATION OF HISTORIC RETURNS TO
MEASURE RISK
EXAMPLE
Paolo is evaluating the possibility to invest in stocks from company X. He made a list
of the return of such security from the last five years. What is the risk associated with
this security?
• Year Holding Period Return
•
•
•
•
•
1
2
3
4
5
10%
30%
-20%
0%
20%
RA = 8%
Variance
• s2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(208)2]/5
•
= [4+484+784+64+144]/5
•
= [1480]/5
• 17,2
= 296
=
7
Standard deviation
Building portfolios : definitions
E(Ri)
Expected return of stock i
Measures central tendency of a variable casuale (i.e the return ), express its
mean and it is the sum of the multiplication of the possible values of the
variable times its respective probabilities
σi
σij
Risk (standard deviation ) of stock i
Measures the level of dispersion of the distribution of a causal
variable(i.e. the return) from its expected valure. It is the possibility of
realizing a return different from the expected one
Correlation between stocks i and j
Measures the relationship between two casual variables
The standard measures for risk are variance and standard deviation
Concepts
• To evaluate
risk, one
has to
quantify it
• However,
there is no
perfect
way of
measuring
risk
• In finance,
the most
commonly
used
method
includes:
Variance
(σ2 or VAR)
Standard
deviation
(σ)
Descriptions
•
The average of squared deviations around
the mean:
2
2
(R1  R )  (R 2  R )  ...  (R T  R )2
σ or VAR 
N -1
where R1 is the actual return and R
Usually you
is the expected return and N is
use N-1 when
the number of observations
there are
observations
from a sample
Square root of variance
(and not actual
Volatility is measured by
population, in
standard deviation of annual
which case N
returns
is used)
2
•
•
σ  VAR
Deviations are squared and
then square-rooted in order
to prevent them from cross
cancelling as a result of
having both positive and
negative numbers
9
Historical share performance shows that returns tend to distribute around an
average
• Plotting the
return of
large US
companies of
each year
from 1926 to
2002, it can
be observed
that returns
tend to be
distributed
around an
average
10
•
2000
1988
1997
1990
1986 1999 1995
1981 1994 1979 1998 1991
1977 1993 1972 1996 1989
1969 1992 1971 1983 1985
1962 1987 1968 1982 1980
1953 1984 1965 1976 1975
1946 1978 1964 1967 1955
2001 1940 1970 1959 1963 1950
1973 1939 1960 1952 1961 1945
2002 1966 1934 1956 1949 1951 1938 1958
1974 1957 1932 1948 1944 1943 1936 1935 1954
1931 1937 1930 1941 1929 1947 1926 1942 1927 1928 1933
-60% -50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80%
A similar
frequency
distribution
is also
observed in
small
company
shares
La costruzione dei portafogli possibili
Distribuzione normale
Probabilità = 2.5%
95% Probabilità
Ampiezza2σ
Valore
atteso
Probabilità = 2.5%
Se il campione è sufficientemente popolato, gli eventi ( ad es. i rendimenti) si distribuiranno normalmente
The probability to
be between the
mean plus or
minus 1 standard
deviation
• If we were to keep on
generating observations for a
long time period, the
aberrations in the sample
would disappear, and the
actual historical distribution
would start to look like the
underlying theoretical
(normal or Gaussian)
distribution
• Normal distribution looks like
a bell-shaped curve
The probability to
be between the
mean plus or
minus 2 standard
deviations
12
The probability to
be between the
mean plus or
minus 3 standard
deviations
Building possible portfolios
How you do it :
• estimate expected return , risk and correlation (covariance ) for all considered stocks
with :
E(Ri) => expected return of stock i
σi
=> Risk (standard deviation ) of stock i
σiJ
=> correlation between stocks i and j
xi
=> vector of weights
• creation of possible portfolios combinind various stocks
• Determination of of expected return and risk of each portfolio and in particular :
E(RP) = Σi xi E(Ri)
=> expected return of portfolio
σP = Σi ΣJ xi xJ σiJ
=> Risk of portfolio
RISK
RISKS ARISING FROM FINANCIAL INSTRUMENTS
BEWARE BLACK SWANS !
to think that risk factors follow a a normal distribution UNDERVALUES extreme market movements
real life distribuion have fatter tails