The purpose of this report is to analyze an equally-weighted portfolio of two US financial
companies - AIG and Wells Fargo(WF), combined portfolio (portfolio) and market portfolio (SPY)
through the below calculation for 3 periods (Pre-crisis period , Crisis Period and Post-crisis period):
(1) Mean and Stdev
(3) Correlation Coefficients
(4) One-day 99% VaR (Normal distribution)
(5) One-day 99% VaR (Historical simulation)
(6) One-day 99% Expected Shortfall (Normal distribution)
(7) One-day 99% Expected Shortfall (Historical simulation)
Mean and Standard Deviation (Stdev)
In the Pre-crisis Period, the mean of expected return of SPY is 0.0537% and the stdev is 0.64418%.
SPY had a highest return with lowest stdev between AIG, WF and portfolio. Therefore the
performance of AIG, WF and portfolio were below than SPY in Pre-crisis Period.
During the financial crisis period 2007–2009, the mean return of SPY and AIG are negative,
especially for AIG, the return is -0.3774%. AIG was suffered a liquidity crisis because many banks
were downgrade of its credit rating. Although the negative mean return of SPY and AIG were
recorded, WF had a positive mean return of 0.1100% because it received $25billion from US
Government and its successful on the acquisition of Wachovia. The mean of portfolio is a negative
-0.1337% although WF had a strong positive return in crisis period.
In the Post-crisis Period, the mean of AIG (0.1699%), WF (0.0702%) and portfolio (0.1201%) are all
higher than SPY (0.0647%) and the stdev of AIG (4.7654%), WF (2.1895%) and portfolio (3.0345%)
are also higher than SPY (1.1735%). All of the results in Post-crisis Period are higher return with
higher stdev. The strong mean return of AIG is because of its pretty smooth on the transition back
to private ownership in Post-crisis Period.
The Beta of a stock or a portfolio is to measure the market risk. The market itself has a beta of 1.0
and SPY is usually used as the proximity of the overall financial market in US. The interpretations
of beta are explained for different period.
During pre-crisis period, β value of AIG, WF and portfolio is 0.7481, 0.8212 and 0.7846
respectively. As the value is 0 < β < 1, it implied that the movement of the asset is generally in the
same direction as, but less than the movement of SPY. Also, it reflected that they are positively
related to the SPY and poses less risky but generally offers lower returns.
During crisis period, β value of AIG, WF and portfolio is 2.0944, 1.7962 and 1.9453 respectively;
meanwhile, during post-crisis period, β value of AIG, WF and portfolio is 1.6772, 1.4727 and
In both periods, as β value is larger than 1, it implied that the movement of the asset is in the
same direction as, but more than the movement of the SPY. With the high beta values during
the crisis period (from 1.7962 to 2.0944), it means that both AIG and WF are higher volatile and
thus riskier for the period concerned. Also, it is positively related with SPY and with high risk but
provide for higher returns potentially.
Correlation coefficient can range from -1.00 to +1.00. The correlation is the average product of the
standard scores for the cases on two stocks, and since the stdev of standardized data is 1.00, then
if the two standardized variables positively and perfectly, the average of their products across the
cases will equal 1.00.
The correlation coefficient between portfolio and AIG was increased from 0.8599 to 0.9465 which
implied that strong positive relationship and was increasing from the period of pre-crisis to post- crisis.
Meanwhile, the correlation coefficient between portfolio and SPY was decreased from 0.7187
to Although we found the historical simulation is generally...
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