The Features of Building a Portfolio of Trading Strategies Using the SAS OPTMODEL Procedure
Abstract
:1. Introduction
2. Materials and Methods
- Fixed amount of risk-admissible losses of the strategies portfolio:
- The sum of all proportions of investments in strategies does not exceed one (i.e., 100%).
- The proportion of investments in each portfolio strategy cannot be negative:
- Fixed amount of profitability by the strategies portfolio must be not less than the profit R.
- The sum of all proportions of investments in strategies does not exceed one (i.e., 100%).
- The proportion of investments in each portfolio strategy cannot be negative:
- the possibility for formulating the models in intuitively understandable way;
- support of explicit usage of the standard SAS functions;
- direct call of linear, nonlinear, quadratic, and mixed-integer-number algorithms for the solution search algorithms;
- support of fast prototyping for the user optimization algorithms including authorized problems;
- the possibility for executing other SAS codes inside of PROC OPTMODEL using the SUBMIT block;
- the algorithms for solving nonlinear optimization problems, including the method of inner point with confidence region and linear search, the method of active set, and the possibility for Multistart;
- quadratic nonlinear optimization with a new solution algorithm for specific large-scale optimization;
- multiflow execution of the process being used;
- conditional optimization with support of planning and resource distribution.
3. Results and Discussion
- information sharing between the trading robot and the exchange takes place with a certain delay, the duration of which is determined by many technical parameters of the computer network, but not exceeding 15 s; the time that, as shown by our experiments in 2015–2018, experiments are sufficient to process agreements on the buying and selling of cryptocurrency;
- storing of aggregate indicators, in contrast to transactional agreements, allows us to speed up the performing of necessary calculations, which in turn saves computing resources, as well as the time required for decision making.
- the vector of profitability of each of the strategies during the month;
- covariance matrix of profitability change of all strategies.
Algorithm 1: MACRO OPT_MODEL. |
MACRO OPT_MODEL; %let LAST=LAST_&&&CURRENCY_PAIR_&i_pair.; %letResult=Result_&&&CURRENCY_PAIR_&i_pair.; %let OUTCORR=OUTCORR_&&&CURRENCY_PAIR_&i_pair.; %let EXPECTED_RETURNS=EXPECTED_RETURNS_&&&CURRENCY_PAIR_&i_pair.; %letCovariance_Matrix=Covariance_Matrix_&&&CURRENCY_PAIR_&i_pair.; %letcode=; data&EXPECTED_RETURNS. (KEEP=NameReturn); set&LAST.; LengthName $18. Return 8; IF profit0 > 0 THEN DO; callsymput(“code”,symget(“code”) !!”diff_”!!TRIM(LEFT(strategy_id))!!” “); Name=“diff_”!!TRIM(LEFT(strategy_id)); Return=profit0; output; END; run; proccorrdata=&Result. noproboutp=&OUTCORR./** storeresults **/ nomiss/** listwisedeletionofmissingvalues **/ cov NOPRINT; /** includecovariances **/ var&code.; run; data&Covariance_Matrix.; set&OutCorr. (rename = (_NAME_=Name) where = (_TYPE_=‘COV’)); keepName &code.; run; /* ------- OPT MODEL ------- */ /* --------- TYPE = 0 ----------------------- */ %IF &TYPE = 0 %THEN %DO; procoptmodel; /* declaresetsandparameters */ set<str> ASSETS; numreturn {ASSETS}; numcovariance {ASSETS, ASSETS}; /* readdatafrom SAS datasets */ readdata&EXPECTED_RETURNS. into ASSETS=[Name] return; readdata&Covariance_Matrix. into [Name] {j in ASSETS} < covariance[Name,j] = col(j)>; /* declarevariables */ varProp {ASSETS} >= 0; /* declareconstraints */ conMy {j in ASSETS}: Prop[j] <= &max_share.; conPortfolio: sum {j in ASSETS} Prop[j] = 1; conVariance: sum {i in ASSETS, j in ASSETS} covariance[i,j] * Prop[i] * Prop[j] <= &expected_risk; /* declareobjective */ maxExpectedReturn = sum {j in ASSETS} return[j] * Prop[j]; solve; print {j in ASSETS: Prop[j] > 1 × 10−4} Prop {j in ASSETS: Prop[j] > 1 × 10−4} return; printVariance.ubVariance.dual; /* writedatato SAS datasets */ createdatapie_datafrom [Name] = {j in ASSETS: Prop[j] > 1 × 10−4} Amount = Prop; quit; run; %END; /* --------- TYPE = 1 ----------------------- */ %IF &TYPE = 1%THEN %DO; procoptmodel; /* declaresetsandparameters */ Set < str > ASSETS; numreturn {ASSETS}; numcovariance {ASSETS, ASSETS}; /* readdatafrom SAS datasets */ readdata&EXPECTED_RETURNS. into ASSETS = [Name] return; readdata&Covariance_Matrix. into [Name] {j in ASSETS} < covariance[Name,j] = col(j)>; /* declarevariables */ varProp {ASSETS} >= 0; /* declareconstraints */ conPortfolio: sum {j in ASSETS} Prop[j] = 1; conMinimum_return: sum {j in ASSETS} return[j] * Prop[j] >= &min_return; /* declareobjective */ minExpectedRisk = sum {i in ASSETS, j in ASSETS} covariance[i,j] * Prop[i] * Prop[j]; solve; print {j in ASSETS: Prop[j] > 1 × 10−4} Prop {j in ASSETS: Prop[j] > 1 × 10−4} return; printMinimum_return.dual; /* writedatato SAS datasets */ createdatapie_datafrom [Name] = {j in ASSETS: Prop[j] > 1 × 10−4} Amount = Prop; quit; run; %END; /* --------- Normalizationresult ----------- */ /* chooseonlystrategieswithappropriateshare */ procsql; createtable pie_data_2 AS selectName, Amount/(sum(Amount)) AsAmountfrom WORK.PIE_DATA; quit; run; data pie_data_3; set pie_data_2; IF Amount >= symgetn(“MIN_SHARE”); RUN; procsql; createtableAmount_Prop_&&&CURRENCY_PAIR_&i_pair. AS selectName, Amount/(sum(Amount)) AsPropformat=Percent8.2 from WORK.pie_data_3; quit; run; dataAmount_Prop_&&&CURRENCY_PAIR_&i_pair.; Formatcurrency_pair $CHAR10.; setAmount_Prop_&&&CURRENCY_PAIR_&i_pair. (Rename = (Name = strategy_id)); currency_pair = “&&&CURRENCY_PAIR_&i_pair.”; run; procprintdata = Amount_Prop_&&&CURRENCY_PAIR_&i_pair.; run; %MEND OPT_MODEL; |
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Proportion of Gaps in the Time Series | Proportion of Hourly Intervals with the Appropriate Level of Gaps | Proportion of Daily Intervals with the Appropriate Level of Gaps |
---|---|---|
0–20 | 80.96 | 78.69 |
20–50 | 6.82 | 10.66 |
50–80 | 4.99 | 4.92 |
80–100 | 7.23 | 5.74 |
Name of the Model | RMSE Value | |
---|---|---|
on a 15 min Frame | on a Daily Frame | |
Seasonal Exponential Smoothing | 1.16 | 24.32 |
Winters Method—Additive Version | 1.17 | 17.01 |
Damped-Trend Linear Exponential Smoothing | 1.09 | 15.65 |
Double (Brown) Exponential Smoothing | 1.35 | 18.57 |
Linear (Holt) Exponential Smoothing | 1.11 | 16.45 |
Multiplicative Seasonal Smoothing | 1.18 | 19.75 |
Simple Exponential Smoothing | 1.09 | 16.71 |
Winters Method—Multiplicative Version | 1.21 | 21.66 |
Strategy | Month of 2018 | Month of 2019 | |||||||
---|---|---|---|---|---|---|---|---|---|
July | August | September | October | November | December | January | February | March | |
469 | 25.45 | −17.34 | 31.13 | 4.90 | 11.01 | 3.88 | 2.82 | −2.43 | −0.59 |
470 | 25.18 | −30.21 | 26.84 | 6.03 | 28.32 | 7.40 | 3.76 | −1.95 | 3.55 |
471 | 41.07 | −24.59 | 31.55 | 7.85 | 21.51 | 1.09 | 8.93 | −0.02 | 3.55 |
472 | −0.79 | 20.04 | 21.66 | 4.46 | 45.91 | 35.38 | 13.87 | 19.50 | 9.55 |
473 | −16.02 | 27.37 | 26.55 | −1.13 | 56.75 | 28.96 | 16.29 | 16.83 | 10.71 |
474 | −24.02 | 22.84 | 22.70 | −3.75 | 59.49 | 26.74 | 12.44 | 17.58 | 10.71 |
475 | 22.39 | −0.07 | 4.23 | 4.05 | −44.52 | 3.94 | 14.31 | 4.09 | −10.97 |
476 | 10.28 | 27.35 | 9.63 | −1.71 | −52.11 | −6.10 | 17.07 | 0.94 | −0.05 |
477 | 5.64 | 19.85 | 8.03 | −12.34 | −48.66 | −0.36 | 18.36 | 1.44 | −4.08 |
478 | 32.53 | −26.37 | 31.19 | 4.53 | 15.10 | 12.14 | 10.40 | −8.55 | 1.45 |
479 | 33.90 | −28.80 | 33.22 | 10.90 | −0.85 | 12.15 | 6.02 | −7.09 | 5.58 |
480 | 42.74 | −29.53 | 31.34 | 8.88 | −7.22 | −6.97 | 13.24 | −1.62 | 5.58 |
Strategy | Month of 2018 | Month of 2019 | ||||||
---|---|---|---|---|---|---|---|---|
August | September | October | November | December | January | February | March | |
469 | 17.67 | |||||||
470 | 22.19 | |||||||
471 | 19.45 | 60.81 | ||||||
472 | 19.11 | 18.98 | 31.66 | 22.11 | 68.07 | 44.9 | ||
473 | 36.82 | 6.35 | 3.69 | 27.52 | ||||
474 | ||||||||
475 | 42.81 | 24.92 | 48.89 | 31.93 | 25.31 | |||
476 | 6.06 | 29.72 | ||||||
477 | 18.25 | 38.01 | 27.64 | 72.48 | ||||
478 | 4.39 | 13.39 | ||||||
479 | 16.75 | 0.05 | ||||||
480 | ||||||||
Cyмa | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
Year | Month | Profitability by Investment Portfolio, % | Capital Increase per 1 Dollar Invested in Bitcoin, Dollars |
---|---|---|---|
2018 | August | −7.47 | −0.07 |
September | 17.56 | 0.09 | |
October | −0.56 | 0.08 | |
November | −3.06 | 0.05 | |
December | 11.18 | 0.17 | |
2019 | January | 14.01 | 0.40 |
February | 5.67 | 0.41 | |
March | 1.50 | 0.43 |
Year | Month | The Price of Bitcoin, Dollars | Standard Deviation | ||
---|---|---|---|---|---|
Average Monthly | Minimum | Maximum | |||
2018 | July | 7335.16 | 6113.2 | 8437.4 | 713.04 |
August | 6608.63 | 5960.2 | 7617 | 372.28 | |
September | 6565.78 | 6119.3 | 7410.2 | 314.27 | |
October | 6539.58 | 6226.9 | 7017.6 | 148.68 | |
November | 4800.98 | 3691.5 | 6578.4 | 930.48 | |
December | 3793.42 | 3239 | 4384 | 278.44 | |
2019 | January | 3754.63 | 3431 | 4157.5 | 187.20 |
February | 3778.44 | 3434.5 | 4219.6 | 214.75 | |
March | 3991.56 | 3776.8 | 4104.2 | 78.18 |
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Terentiev, O.; Prosiankina-Zharova, T.; Savastiyanov, V.; Lakhno, V.; Kolmakova, V. The Features of Building a Portfolio of Trading Strategies Using the SAS OPTMODEL Procedure. Computation 2021, 9, 77. https://doi.org/10.3390/computation9070077
Terentiev O, Prosiankina-Zharova T, Savastiyanov V, Lakhno V, Kolmakova V. The Features of Building a Portfolio of Trading Strategies Using the SAS OPTMODEL Procedure. Computation. 2021; 9(7):77. https://doi.org/10.3390/computation9070077
Chicago/Turabian StyleTerentiev, Oleksandr, Tatyana Prosiankina-Zharova, Volodymyr Savastiyanov, Valerii Lakhno, and Vira Kolmakova. 2021. "The Features of Building a Portfolio of Trading Strategies Using the SAS OPTMODEL Procedure" Computation 9, no. 7: 77. https://doi.org/10.3390/computation9070077
APA StyleTerentiev, O., Prosiankina-Zharova, T., Savastiyanov, V., Lakhno, V., & Kolmakova, V. (2021). The Features of Building a Portfolio of Trading Strategies Using the SAS OPTMODEL Procedure. Computation, 9(7), 77. https://doi.org/10.3390/computation9070077