ORANGE COUNTY FINANCIAL CASE-Value At Risk Calculations
Please complete the project by using the information in the attached excel file below:
Required:
1. Use the excel file to compute the following informations and provide workings in the excel file-for e.g, calculation of z values, dy, VAR ect…Draw histogram ect..
2. Write a short report of max 3 pages to explain your answers on excel.
Section 1-Duration approximation
The average duration of the securities is about 2.74 years for a portfolio with leverage ratio of 2.7. The portfolio size is $20.25 billion with capital of $7.5 billion. The interest rates went up about 3% in 1994
Question 1: Compute the loss predicted by the duration approximation and compare your result with the actual loss of $1.64 billion.)
Section 2-Computation of portfolio VAR
The monthly yield data is provided. Using this information (last 5 years monthly rate changes (60 points)) to compute the portfolio VaR as of December 1994. Risk should be measured over a month at the 95% level.
Question 2: Report the distribution and compute the VaR using a Delta-Normal method.
Question 3: Report the distribution and compute the VaR using a Historical-Simulation method.
Question 4: Compare VaR obtained by these two methods
Section 3-Interpretation of VAR
Question 5: Convert the monthly VAR into an annual figure. Is the latter number consistent with the $1.6 billion loss?
Question 6: From December 1994 to December 1995, interest rates fell from 7.8% to 5.25%. Compute the probability of such an event (rates fell more than this) based on the Delta-Normal method.
Case Study: Orange County Bankruptcy
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016
Case Study: Orange County
Bankruptcy
FIN 5623 Final Project
1
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016
Orange County Bankruptcy Case
âš« https:
financetrain.com/orange-county-case
âš« https:
merage.uci.edu/~jorion/oc/case.html
2
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016
Introduction
âš« $7.5 billion Capital and was leveraged to $20.5 billion
âš« Mostly 5-year agency bonds (Fannie, Freddie)
âš« Bo
owing in short term (Repo) with rate < 3% and
investing in medium maturity bond with rate ~ 5.2%
âš« In December of 1994, the average duration of individual
security is 2.74 year, and the leverage ratio is 2.7. The
effective duration is 7.4 year.
âš« In Fe
uary 1994, Fed started a series of six consecutive
interest rate increases and rates went up by about 3%
âš« The portfolio had lost $1.5 billion by Nov. 1994 and
finally went to bankruptcy.
3
Interest Curve 12/1993
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016 4
Interest Rates Movement
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016 5
Repurchase Agreement (Repo)
âš« A Repo is a form of short-term bo
owing for dealers -
- a dealer sells government securities to investors
and buys them back the following day at a slightly
higher price. It can be viewed as a collateral loan
âš« A Reverse Repo is the opposite of a Repo (ML had a
everse Repo with Orange County)
âš« Repo have Term Repo and Open Repo
âš« If the collateral falls in value, a margin call can take
effect to ask the bo
ower to amend the securities
offered.
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016 6
Risk Factors and Loss
Distribution
âš« The value of financial instruments depends on a few
fundamental factors – risk factors, such as interest rates,
inflation, exchange rate
?? = ?(?, ??)
âš« The randomness of loss distribution is due to the change
of risk factors ??+1: = ??+1 − ??
??+1 = − ? ? + 1, ?? + ??+1 − ? ?, ?? = ? ? (??+1)
âš« Linearization of Loss Distribution
??+1 ≈ −(?? + ??
′ ⋅ ??+?)~?(−?? − ??
′ ⋅ ?, ??
′Σ??)
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016 7
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016
Interest Rate Sensitivity
âš« Fixed-income assets valuation:
?? = ?(?, ??)
⚫ Interest rate sensitivity – Effective Duration:
? = −
1
??
? ?, ?? + Δ? − ? ?, ?? − Δ?
2Δ?
Δ?
?
≈ −? ∗ Δ?; ? ≈ ? ∗ ? ∗ ??
âš« Duration and VaR of investments
???$? = ? ∗ ? ∗ ?????
8
Methods to Measure VaR
âš« Delta-Normal Method
âš« Risk factor and portfolio return are normal distributed
âš« Going back 5 years to compute distribution parameters for all risk
factors
âš« Apply to the portfolio to compute VaR
âš« Historical-Simulation Method
âš« Take 5 years of historical data of risk factors as the realization of
the probability distribution of the risk factor to compute VaR (non-
parametrized estimation)
âš« Apply to the portfolio to compute VaR
âš« Annualized VaR
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull 2016 9
Final Project (1)
âš« Duration approximation
âš« The average duration of the securities is about 2.74
years for a portfolio with leverage ratio of 2.7
âš« The portfolio size is $20.25 billion with capital of $7.5
illion
âš« The interest rates went up about 3% in 1994
âš« Compute the loss predicted by the duration
approximation and compare your result with the actual
loss of $1.64 billion.
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull XXXXXXXXXX
Final Project (2)
âš« Computation of portfolio VAR
âš« The monthly yield data is provided. Using this
information (last 5 years monthly rate changes (60
points)) to compute the portfolio VaR as of December
1994. Risk should be measured over a month at the
95% level.
âš« Report the distribution and compute the VaR using a
Delta-Normal method.
âš« Report the distribution and compute the VaR using a
Historical-Simulation method.
âš« Compare VaR obtained by these two methods
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull XXXXXXXXXX
Final Project (3)
âš« Interpretation of VAR
âš« Convert the monthly VAR into an annual figure. Is the
latter number consistent with the $1.6 billion loss?
âš« From December 1994 to December 1995, interest
ates fell from 7.8% to 5.25%. Compute the probability
of such an event (rates fell more than this) based on
the Delta-Normal method.
âš« It seems that both in 1994 and 1995, interest rate
swings were particularly large relative to the historical
distribution. Suggest two interpretations for this
observation.
Fundamentals of Futures and Options Markets, 9th Ed, Ch 25, Copyright © John C. Hull XXXXXXXXXX