EurOil Index
Created and maintained by Dimitrios
D. Thomakos © 2007/2008
Technical Notes, Commentary and Contributions (click on links
below)
Last updated:
[1.] Global
Minimum Variance Portfolio vs. Rotation
[2.] Rotational
Forecasts and Real Time Trading
[3.] Sign
Forecasting using Realized Volatility , updated
Global
Minimum Variance Portfolio vs. Rotation
By Timotheos Angelidis, Department of
Economics,
Portfolio managers try to minimize the risk of their portfolio relative
to a benchmark and set a limit on the tracking error volatility, which is
defined as the standard deviation of the difference between the portfolio, Rp, and the
benchmark, Rb, return.
Given that each fund manager may use a different benchmark in order to
be evaluated, we consider the Global Minimum Variance (GMV) portfolio of the
two assets Oil and the Euro as the benchmark portfolio. The weights of the GMV
portfolio are calculated as the solution to the problem:
Minimize with
respect to weights w the portfolio
variance Vp = wTSw subject to wT1 =1 (weights sum-up to one)
where S is the variance covariance matrix of the two returns
and 1 is a column vector of ones.
The GMV
portfolio overweighs the Euro position (weight 95%) as the annual standard
deviation of the weekly changes of Oil is almost 4 times greater than that of
Euro. The annualized Tracking Error volatility ranges from 2%, if the portfolio
is consisted only from the Euro position, to 38% if the portfolio is consisted
only from the Oil position. These tracking error volatility numbers correspond
to the cases of complete rotation of the two assets that are considered in the
simulated trading exercise. The detailed results are presented in the following
graph.
Rotational
Forecasts and Real Time Trading
By Greg Siourounis, Department of
Economics,
1.
Introduction
Dimitrios Thomakos has recently launched a very
interesting approach to financial assets forecasting. Going to the heart of the
main problem when one constructs a portfolio of more than one asset, he
proposes a novel methodology on future price movements. This methodology
abstracts from point forecasts and focuses on forecasting future trends.
Another novelty o the methodology is that it uses the levels of the series
under investigation and not the log returns. This can be achieved by studying
the dynamics of the series using near-unit root econometrics. Based on the
developed methodology, the author launched a weekly trading strategy for EUR
and Brent Crude Oil for a
2. Transaction costs
Real time trading has one enemy ceteris
paribus: transaction costs. Although they have fallen monotonically over the
last 7 years, after the birth of the EUR (for currencies see Papaioannou,
Portes, and Siourounis (2006)) they still prove difficult to beat if one trades
frequently (for currency markets see Burnside,
Eichenbaum, Kleshchelski,
Rebelo
(2006, 2007)). Apart from the different sizes that a trader faces when
initiates positions in various financial assets, an important element is when
she starts trading. In the presence of transaction costs, the decision to
invest in some new asset allocation different from the present one, involves
the exit from the current positions and the entry to the new one. This is
costly and should be taken into account when trading strategies are proposed.
In Thonakos’ framework this can be done
relatively easy since the forecasting exercise gives rise to a rotational
allocation, meaning that for two assets (EUR and Brent Crud Oil) the trader is
fully invested only in one of them at each point in time. The current strategy
does not allow short selling so in essence the problem reduces to the
accommodation of one Bid and one Ask price (if rotation for next period is
suggested by the trading strategy). The investor faces the bid price to exit
from the current asset and the ask price to enter the new one. For EUR/USD the
current real time bid/ask spread is approximately 2pips (source: SAXO Bank
Plc). For Brent Crude oil is 100 bps (source: SAXO Bank Plc). So a movement, for
example from EUR into Oil can cost 2bps, whereas a new rotation from Oil to EUR
can cost an additional 102bps. For leveraged positions this can be a very large
amount but the strategy is saved by the fact that gives weekly signals that do
not suggest rotation every week. It is obvious, however, that transaction costs
erode the performance of the suggested strategy and in order to have a clear
view of its profitability, transaction cost must be included.
3. Cash
Basic portfolio analysis suggests that a trader
should be able to decide how much of her portfolio should be invested in risky
assets, like stocks, and how much in less risky assets (like cash or short term
money instruments - often mentioned as riskless assets). In the present context
of fully invested traders, this amounts to stay out of the market when the
trading strategy suggests rotation to cash. A relevant question is if cash is
an interest bearing asset, no interest bearing asset, or borrowed asset. These
three cases have very different implications regarding the risk profile of an
investor and should be analyzed separately. In the current strategy the cash
asset is not borrowed and it does not bear any interest. Note also that if we
assume that if on the top we assume that buying EUR is identical in buying 1
week EUR deposits then there is also an issue of interest rate differentials.
Another issue that stems from the use of interest bearing or borrowed cash
asset is the investment horizon vs. the forecasting-trading horizon. It is
obvious that if the two match then the only issue is if one uses the correct
interest rate from the money market as a return or cost for holding cash. In
the event that the two do not agree the issue becomes more complicated and
beyond the current note.
4. Base currency
In relation to the inclusion of the cash asset
is the type of the base currency. The 1 week USD Libor currently rests at 4.75%
whereas the 1 week EURIBOR rests at 3.96%. It is obvious that if cash is
interest or cost bearing the base currency makes considerable difference
depending in which currency the investor is based upon. A solution to this
issue is not obvious since many investors are cash-based to the country of
their residence. A second issue relates to the fact that any investor based on a
currency different form the dollar, faces FX risk when investing in Oil since
she has to first convert her EUR into USD and then buy the Oil contract. A
solution to this second problem can be the use of 1 week FX Forwards to hedge
against FX movements. This, off course will increase the trading cost of the
suggested strategy and should be incorporated in the reported back testing
results.
5. Interest rate announcements
As far as the FX market is involved in a
trading portfolio, interest rate announcements play a crucial role, especially
in a weekly basis. Any week that bears rate announcements from the Fed, ECB and
the BOE must be treated accordingly. In Thomakos’ context this can be resolved
in two ways: the first one is to treat these weeks individually by augmenting
the trading rule to give rotational signals only if strong evidence exists for
the direction of the trend. The second is something simpler and aims to
increase the strategy’s Sharpe ratio. It involves the recommendation to stay in
cash for the week a rate decision is expected.
6. Concluding remarks
EUROIL is a first attempt to show the strength
of well researched econometric technique that pushes the frontier of profitable
investment strategies. This note aims to give a niche of the issues involved
when these strategies are contrasted to real time trading. Future research
should contrast this methodology of forecasting asset trends and constructing
asset portfolios to traditional portfolio construction techniques that have
repeatedly proven very poor in replicating successfully the real investment
process.
References
[1.] Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 2007. "The Returns to Currency Speculation
in Emerging Markets," NBER Working Papers 12916,
National Bureau of Economic Research
[2.] Craig Burnside & Martin Eichenbaum & Isaac Kleshchelski &
Sergio Rebelo, 2006. "The Returns to Currency Speculation,"
NBER Working Papers 12489,
National Bureau of Economic Research
[3.] Papaioannou, Elias
& Portes, Richard & Siourounis, Gregorios, 2006. "Optimal currency
shares in international reserves: The impact of the euro and the prospects for
the dollar," Journal of the Japanese and
International Economies, Elsevier, vol. 20(4), pages 508-547,
December
Sign
Forecasting using Realized Volatility
By Viki Skintzi, Department of
Economics,
Besides price and return forecasting an interesting issue in financial
time series is the direction-of-change forecasting. Recent theoretical and
empirical work has revealed a direct link between return sign forecasting and
volatility forecasting. Sing forecasting can be easily applied in a trading
strategy that rotates between two assets. By forecasting the sign of the next
period return for Eurodollar and oil as well as the sign of the difference
between the two assets returns such strategy signals rotation among Eurodollar,
oil and possibly cash. To empirically apply this approach I constructed the
weekly realized volatility of the two assets, using the sum of daily squared
returns, and then applied a simple AR model for computing volatility forecasts
and using them for constructing trading signals. As an example, see below the
trading recommendations from
Table 1: 68 weeks estimation period
|
Trading recommendation for Monday |
Asset |
Success in Direction |
Realized Return of Strategy |
Cumulative value of 1$ |
|
week of |
Oil |
+ |
3,53 |
1,0353 |
|
week of |
Euro |
- |
-1,39 |
1,0214 |
|
week of |
Euro |
+ |
0,39 |
1,0253 |
|
week of |
Euro |
- |
-2,37 |
1,0016 |
|
week of |
Euro |
- |
0,28 |
1,0044 |
|
week of |
Oil |
+ |
2,26 |
1,0270 |
Table 2: 268 weeks estimation period
|
Trading recommendation for Monday |
Asset |
Success in Direction |
Realized Return of Strategy |
Cumulative value of 1$ |
|
week of |
Oil |
+ |
3,53 |
1.0353 |
|
week of |
Oil |
- |
-7,70 |
0.9583 |
|
week of |
Oil |
- |
-0,59 |
0.9524 |
|
week of |
Oil |
+ |
3,37 |
0.9861 |
|
week of |
Oil |
+ |
1,40 |
1.0001 |
|
week of |
Oil |
+ |
2,26 |
1.0227 |
References
[1] Christoffersen P.F. and F.X. Diebold (2006)
Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics,
Management Science, 52, 1273–87.
[2] Christoffersen P.F., F.X. Diebold, R.S.
Mariano, A.S. Tay and Y.K. Tse (2006) Direction of-Change Forecasts Based on
Conditional Variance, Skewness and Kurtosis Dynamics: International Evidence,
PIER Working Paper No. 06-016.