An analysis of Volatility Modelling and Hedging: A case study of Goldman Sachs

1. VOLATILITY
MODELLING AND
HEDGING ANALYSIS
KEHINDE OGUNJEMILUSI

2. Content:
WHY GOLDMAN SACH?
GRAPHICAL ANALYSIS- PRICES,
RETURNS, ABSOLUTE RETURN
OVER A 5 YEAR PERIOD
ECONOMICAL AND
STATISTICAL ANALYSIS
VOLATILITY MODELLING
(GARCH MODEL-EXCEL &
EVIEWS)
HEDGING ANALYSIS- STRATEGY
AND OUTCOME
CONCLUSION

3. WHY GOLDMAN SACH?
 Leading global investment banking, securities and investment management firm.
 “35th-largest bank in the world by total assets ($916.78 B)”1
 Ascertain the impact of the 1Malaysian Development Berhad (1MDB) scandal on
it’s stock volatility.

4. GRAPHICAL ANALYSIS

5. ECONOMICAL AND STATISTICAL ANALYSIS
ECONOMICAL ANALYSIS STATISTICAL ANALYSIS
Bankers from Goldman Sachs helped Malaysia set up a $6.5
billion bond fund, and to put it mildly, it didn't turn out well. At
least $4.5 billion was taken from the fund (not by Goldman), and
it could cost the bank billions of dollars to put the matter behind
it. Malaysia is attempting to recoup billions, and the U.S. Justice
Department is investigating the bank's role in the scandal1.

6. VOLATILITY MODELING
Advantages
 It incorporates Mean reversion
 It has a structure that enables forecasts of the
future level of variance rate to be produced
relatively easily.
 It can be used for updating covariance estimates
and forecasting the future level of covariance
Disadvantages
 The model assumes that positive and negative shocks have the
same effects on volatility. In practice, it is well known that asset
prices responds differently to positive and negative shocks i.e. in
other words, bad news (identified by a negative sign) has the
same influence on the volatility as good news (positive sign) if
the absolute values are the same
Volatility is the degree of variation of a trading price series over a time period. The Garch is a model proposed by Bollerslev in
1986 implemented by using the variance targeting- setting the long-run average volatility equal to the sample variance. The Garch
Model (Excel and Eviews) was applied to model the volatility of Goldman Sachs stock.

7. GARCH MODEL IMPLEMENTATION OUTPUT(EVIEWS &
EXCEL)
.0000
.0001
.0002
.0003
.0004
.0005
.0006
.0007
.0008
.0009
250 500 750 1000 1250
Conditional variance
.000
.004
.008
.012
.016
.020
.024
5 10 15 20 25 30 35 40 45 50 55 60
Conditional variance
VARIABLE MONTHLY DAILY VARIABLE MONTHLY DAILY
C 0.002423 0.000008 ω 0.002262 0.000009
RESID(-1)^2 0.398658 0.069130 α 0.377091 0.082094
GARCH(-1) 0.119143 0.895095 β 0.187316 0.875144
EVIEWSOUTPUT EXCELOUTPUT

8. HEDGING ANALYSIS
AND STRATEGY
STDEV (Risk) DAILY MONTHLY
WTIr 1.46% 2.18%
WTIFr 1.64% 2.37%
No Hedge 1.45% 2.18%
Naïve 0.86% 1.23%
OHR 0.76% 1.12%
 Hedging was applied to reduce the risk and volatility
of the asset.
 Hedging Strategy:
 Examined correlation with other asset to create
optimal portfolio.
 Took a Long position on Spot asset- Goldman Sachs
 Short position on Futures asset- Morgan Stanley.
 Implemented No Hedge, Naïve Hedge and Optimal
Hedge Ratio(OHR) strategy.
MONTHLY DAILY
Correlation 0.852638361 0.857507271
No Hedge 0 0
Naïve 1 1
OHR 0.755617677 0.789622306

9. HEDGING STRATEGY OUTPUT

10. CONCLUSION
 Based on the Garch Model implemented, Goldman Sachs has had volatile years after being plagued by the 1MDB
Malaysian scandal. However, we observed that there exist an improvement in the volatility of it’s stock after the
highest volatility as observed from the graphical analysis( e.g. from the period 17th January to 1st February
2019). This could be linked to the strong Q4 2018 financial result which caused a rebound in its price as well as
the recent management changes to grow as an investment and retail bank while moving away from trading.
While certain risks such as further fines from the 1MDB scandal do exist, investors might have taken the
asymmetric risk to reward ratio as a good buying opportunity1
 In addition, the volatility/risk of the asset was efficiently and effectively managed by the hedging strategy
implemented.(i.e. Optimal Hedge Ratio) and as such minimises the risk that investors are exposed to. The No
hedge strategy however exposes investors to unforeseen risk and loss of funds on the long run.