The future value of a portfolio in thousands of scenarios. Each asset is calibrated on its own price history, the assets move together through their historical correlation, and the result is the distribution of the portfolio’s value period by period, with its Value at Risk and Expected Shortfall. Everything runs in your browser.
1 · Portfolio and pricesⓘ
Start from one of the twelve model portfolios, or load your own price history and positions.
✓Portfolio loaded into the model: Conservative Income Portfolio · 20 positions · 1,000 days of prices
The model portfolios run on synthetic prices, generated for the demonstration with realistic volatility and correlation by asset type. They are illustrative, not market data.
iShares iBoxx $ Investment Grade Corporate Bond ETF
Commercial Paper
222.3
222,303
3.2%
VCIT
Vanguard Intermediate-Term Corporate Bond ETF
Commercial Paper
74.08
111,114
1.6%
MUB
iShares National Muni Bond ETF
Municipal Bonds
52.13
78,192
1.1%
VTEB
Vanguard Tax-Exempt Bond ETF
Municipal Bonds
56.06
168,177
2.4%
MBB
iShares MBS ETF
Asset-Backed Securities
164.46
164,464
2.4%
VMBS
Vanguard Mortgage-Backed Securities ETF
Asset-Backed Securities
169.37
440,366
6.3%
VNQ
Vanguard Real Estate Investment Trust ETF
REITs
587.81
646,593
9.3%
IYR
iShares U.S. Real Estate ETF
REITs
437.39
568,605
8.2%
VTV
Vanguard Value ETF
Style ETFs
277.14
193,998
2.8%
T
AT&T Inc.
Individual Stocks
524.9
2,099,614
30.2%
SO
The Southern Company
Individual Stocks
244.1
292,925
4.2%
PG
The Procter & Gamble Company
Individual Stocks
24.55
19,638
0.3%
XOM
EXXON
Individual Stocks
335.2
335,200
4.8%
IBM
International Business Machines Corporation
Individual Stocks
98.59
49,295
0.7%
MSFT
Microsoft Corporation
Individual Stocks
346.75
104,025
1.5%
GLD
SPDR Gold Shares
Individual Stocks
303.91
106,369
1.5%
Total
6,946,194
100%
2 · Simulationⓘ
Correlation used by the simulation
TLT
IEF
SCHP
VTIP
LQD
VCIT
MUB
VTEB
MBB
VMBS
VNQ
IYR
VTV
T
SO
PG
XOM
IBM
MSFT
GLD
TLT
1.00
0.57
0.60
0.59
0.60
0.58
0.59
0.60
0.60
0.61
-0.05
0.00
-0.03
-0.07
-0.03
-0.01
-0.03
-0.03
-0.02
-0.04
IEF
0.57
1.00
0.62
0.61
0.63
0.62
0.64
0.64
0.59
0.60
0.00
0.01
0.00
-0.06
0.01
-0.01
0.00
-0.01
0.00
-0.01
SCHP
0.60
0.62
1.00
0.66
0.60
0.63
0.67
0.65
0.58
0.64
-0.04
0.03
0.01
-0.05
0.00
0.00
-0.01
-0.02
0.03
0.02
VTIP
0.59
0.61
0.66
1.00
0.59
0.60
0.62
0.66
0.54
0.58
-0.13
-0.10
-0.13
-0.18
-0.14
-0.15
-0.12
-0.15
-0.13
-0.05
LQD
0.60
0.63
0.60
0.59
1.00
0.62
0.63
0.65
0.64
0.62
-0.05
-0.02
-0.04
-0.05
-0.04
-0.02
-0.02
-0.04
-0.02
0.00
VCIT
0.58
0.62
0.63
0.60
0.62
1.00
0.64
0.61
0.57
0.65
-0.05
0.01
-0.04
-0.06
0.00
-0.02
-0.02
-0.08
0.00
0.02
MUB
0.59
0.64
0.67
0.62
0.63
0.64
1.00
0.64
0.61
0.63
-0.03
0.03
0.02
-0.06
0.02
0.01
0.01
-0.04
0.01
-0.01
VTEB
0.60
0.64
0.65
0.66
0.65
0.61
0.64
1.00
0.67
0.63
-0.03
0.00
0.01
-0.06
-0.05
-0.02
-0.04
-0.04
-0.02
-0.02
MBB
0.60
0.59
0.58
0.54
0.64
0.57
0.61
0.67
1.00
0.60
-0.03
0.03
0.00
-0.06
-0.02
-0.01
-0.01
-0.05
0.00
-0.01
VMBS
0.61
0.60
0.64
0.58
0.62
0.65
0.63
0.63
0.60
1.00
-0.04
-0.01
0.00
-0.05
0.01
0.01
0.00
-0.04
0.01
-0.02
VNQ
-0.05
0.00
-0.04
-0.13
-0.05
-0.05
-0.03
-0.03
-0.03
-0.04
1.00
0.33
0.37
0.40
0.38
0.35
0.38
0.38
0.35
0.09
IYR
0.00
0.01
0.03
-0.10
-0.02
0.01
0.03
0.00
0.03
-0.01
0.33
1.00
0.41
0.40
0.41
0.43
0.40
0.38
0.39
0.13
VTV
-0.03
0.00
0.01
-0.13
-0.04
-0.04
0.02
0.01
0.00
0.00
0.37
0.41
1.00
0.45
0.49
0.52
0.48
0.51
0.47
0.20
T
-0.07
-0.06
-0.05
-0.18
-0.05
-0.06
-0.06
-0.06
-0.06
-0.05
0.40
0.40
0.45
1.00
0.50
0.44
0.47
0.48
0.48
0.25
SO
-0.03
0.01
0.00
-0.14
-0.04
0.00
0.02
-0.05
-0.02
0.01
0.38
0.41
0.49
0.50
1.00
0.47
0.51
0.47
0.47
0.25
PG
-0.01
-0.01
0.00
-0.15
-0.02
-0.02
0.01
-0.02
-0.01
0.01
0.35
0.43
0.52
0.44
0.47
1.00
0.47
0.47
0.47
0.20
XOM
-0.03
0.00
-0.01
-0.12
-0.02
-0.02
0.01
-0.04
-0.01
0.00
0.38
0.40
0.48
0.47
0.51
0.47
1.00
0.46
0.45
0.22
IBM
-0.03
-0.01
-0.02
-0.15
-0.04
-0.08
-0.04
-0.04
-0.05
-0.04
0.38
0.38
0.51
0.48
0.47
0.47
0.46
1.00
0.43
0.16
MSFT
-0.02
0.00
0.03
-0.13
-0.02
0.00
0.01
-0.02
0.00
0.01
0.35
0.39
0.47
0.48
0.47
0.47
0.45
0.43
1.00
0.19
GLD
-0.04
-0.01
0.02
-0.05
0.00
0.02
-0.01
-0.02
-0.01
-0.02
0.09
0.13
0.20
0.25
0.25
0.20
0.22
0.16
0.19
1.00
Pearson correlation of the assets’ daily log returns over 999 observations, made consistent before the run if needed. Shocks to the assets are drawn with these coefficients; blue is positive, pink negative.
4 · Choosing a modelⓘ
Two views of which model to trust: the catalogue’s expert scores for the kinds of assets held, and every model run on this portfolio’s own history.
Suitability by asset categoryⓘ
Average of the catalogue’s 0–5 scores for each holding’s category, weighted by value; it covers 100% of the portfolio.
VAR (vector autoregression)
3.95
Regime switching
3.88
Hull-White stochastic volatility
3.52
Geometric Brownian Motion
3.47
in use
GARCH + jump diffusion
3.46
GJR-GARCH (asymmetric)
3.46
Merton jump diffusion
3.46
Kou double exponential
3.46
Heston stochastic volatility
3.41
Variance Gamma
3.37
Ornstein–Uhlenbeck (mean reversion)
3.26
CEV (formerly SABR)
2.95
Same portfolio, history, seed and horizon for every model; up to 200 iterations each.
5 · Validationⓘ
Does the model forecast well on this portfolio, how does it behave under stress, and are there enough iterations? Each tool runs the model chosen in section 2.
At each test date the model is calibrated only on the history up to that date, the portfolio is simulated ahead, and the forecast is set against what really happened.
Horizon 10 days, from the simulation settings; test dates are 10 days apart so the forecasts do not overlap.
6 · Risk attributionⓘ
Where the VaR and Expected Shortfall come from: by asset, sector, category, asset type, country and exchange.
The portfolio is simulated with the model and settings of section 2, keeping each asset’s value at the horizon, so the totals are those of section 3.
Measureⓘ
7 · Portfolio optimizationⓘ
Better weights for the same holdings: lower risk, a better return for the risk, or risk spread evenly.
Every objective is solved on the futures simulated by the model of section 2 — jumps, volatility clustering and fat tails included — for a portfolio bought today and held to the horizon. Only the weights of the current holdings change. Long-only: no short positions.
Expected returnsⓘ
Each asset’s historical return is pulled towards the portfolio average by the share of the differences that is estimation noise. Historical returns are the least reliable input to any optimizer.
Constraintsⓘ
Share of the portfolio that may be traded (one way). Empty: no limit.
✦AI reportsⓘ
Four AI agents write a report from the results on this page, each for a different reader. Run the simulation first; the more of the model comparison, validation and attribution you have run, the more complete the reports.
The reports will draw on:Simulation · not runModel comparison · not runBacktest · not runStress tests · not runConvergence · not runRisk attribution · not runOptimization · not run
Run the simulation (section 2) to write a report.
Technical report
For risk specialists and model validators: every figure, the method, the validation evidence and the limitations.
Regulatory report
For supervisors, internal audit and model-risk management: scope, assumptions, outcomes analysis and numbered findings.
Executive summary
For management and the board: the bottom line, what drives it and what to do, in two minutes.
Plain-language report
For investors with no finance training: what could happen to the money, in everyday words.