### Portfolio Optimization for 20 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Portfolio Optimization for 20 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Problem:
Construct the Optimal Portfolio that:
delivers the target return (mu_Target)
with minimum risk
Minimize the risk of the portfolio (in this case, measured as half the variance)
While maintaining an expected return target of (mu_Target)
By adjusting the investment weights on each asset
Subject to the budget constraint that the weights sum to 1
Method:
Since constraints are equalities => We can use Method Lagrange
Supports up to 20 securities.

Constraints:
No short-selling (ie. No negative weights)

Solution 00:
Basic MPT with only budget constraint that weights sum to 1
Solution 01:
Tweaked solution where no negative weights are allowed,
but budget contraint fails, as sum of weights exceed 1.
Solution 02:
Maintain that no negative weights are allowed,
but normalize weights such that they sum to 1.
This yields a practical solution, but usually unable to meet target return.

### Portfolio Optimization for 10 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Portfolio Optimization for 10 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Problem:
Construct the Optimal Portfolio that:
delivers the target return (mu_Target)
with minimum risk
Minimize the risk of the portfolio (in this case, measured as half the variance)
While maintaining an expected return target of (mu_Target)
By adjusting the investment weights on each asset
Subject to the budget constraint that the weights sum to 1
Method:
Since constraints are equalities => We can use Method Lagrange
Supports up to 10 securities.

Constraints:
No short-selling (ie. No negative weights)

Solution 00:
Basic MPT with only budget constraint that weights sum to 1
Solution 01:
Tweaked solution where no negative weights are allowed,
but budget contraint fails, as sum of weights exceed 1.
Solution 02:
Maintain that no negative weights are allowed,
but normalize weights such that they sum to 1.
This yields a practical solution, but usually unable to meet target return.

### Portfolio Optimization for 5 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Portfolio Optimization for 5 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1

Problem:
Construct the Optimal Portfolio that:
delivers the target return (mu_Target)
with minimum risk
Minimize the risk of the portfolio (in this case, measured as half the variance)
While maintaining an expected return target of (mu_Target)
By adjusting the investment weights on each asset
Subject to the budget constraint that the weights sum to 1
Method:
Since constraints are equalities => We can use Method Lagrange
Supports up to 5 securities.

Constraints:
No short-selling (ie. No negative weights)

Solution 00:
Basic MPT with only budget constraint that weights sum to 1
Solution 01:
Tweaked solution where no negative weights are allowed,
but budget contraint fails, as sum of weights exceed 1.
Solution 02:
Maintain that no negative weights are allowed,
but normalize weights such that they sum to 1.
This yields a practical solution, but usually unable to meet target return.

### Portfolio Optimization for 4 Securities Using Lagrange Multipliers

Construct the Optimal Portfolio that:
delivers the target return (mu_Target)
with minimum risk
Minimize the risk of the portfolio (in this case, measured as half the variance)
By adjusting the investment weights on each asset
Subject to
Expected return target = mu_Target (specified by user)
Weights sum to 1 (ie. fully invested)
Weights can be negative

### Risk: Value-at-Risk (VaR) Calculator for Portfolio of 12 Tickers

This Excel spreadsheet calculates Value-at-Risk (VaR) for a portfolio of up to 12 tickers
Parametric, Historical, Monte-Carlo simulated Value-at-Risk (VaR)
Mean, Standard Deviation, Variance, Correlation, Covariance
Incremental VaR for each ticker in the portfolio (without rebalancing)
Marginal VaR for each ticker in the portfolio (with rebalancing)
Cholesky Decomposition of the covariance matrix using built-in VBA function

It provides the user with one-click solution to download historical data from IB.

### Excel Trading Execution Template for Interactive Brokers (IB) Trader Workstation (TWS)

An Excel VBA template interface for one-click trading execution on Interactive Brokers (IB) Trader Workstation (TWS)..
Fully customizable and open-source VBA code for developers who wish to implement their trading algorithm via the Excel platform.

### Equity Index Participation

Equity Index Participation
Given a specified equity ticker, list the indices which contain it, and the corresponding weight of the ticker within each index.

### Trading Strategy BackTesting (in Excel or Python)

Backtest any strategy for any asset class.
in Excel (.xlsm)
in Python (.ipynb on Google Cloud Platform).
Bloomberg historical data will be provided.

### Derivative Pricing for Interest Rate Derivatives under Heath-Jarrow-Morton (HJM) Framework for Term Structure of Interest Rates with Principal Components Analysis (PCA), Monte Carlo Simulation (MCS), Credit Valuation Adjustment (CVA)

Derivative Pricing for Interest Rate Derivatives
under Heath-Jarrow-Morton (HJM) Framework
for Term Structure of Interest Rates
with
Principal Components Analysis (PCA),
Monte Carlo Simulation (MCS),

Live Price, Historical Prices, Option Chain.
1 Ticker at a time.
1 or All Expiration Dates with 1 click,
Puts or Calls or Both Puts and Calls in a straddle view.
All strikes in ascending order.

Demo Video:

### Option Pricing & Risk (Greeks) Graph Generation Tool

Generate option pricing and risk (Greeks) graphs under the Black-Scholes model.

### Option Pricing & Risk (Greeks) for Digital(Binary) Options on NADEX

Generate digital(binary) option pricing and risk (Greeks) graphs under the Black-Scholes model.

### Option Pricing & Risk (Greeks) for Digital(Binary) Options on NADEX with Scenario Analysis

Scenario Analysis for digital(binary) options and it’s Greeks.

### Option Strategy (2 Legs) P&L Attribution Back-Test

Back-test an option strategy to see how it performs. Understand where it made or lost money.
Supports up to 2 option legs.

### Option Strategy (4 Legs) P&L Attribution Back-Test

Back-test an option strategy to see how it performs. Understand where it made or lost money.
Supports up to 4 option legs.

### Portfolio Construction Tool: Beta Neutral Relative Value

Create a beta-neutral relative-value portfolio of 2 securities.

### Loan Mortgage Monthly Payment Calculator

Simple tool to calculate monthly payments for your loan.
This demonstrates the use of Excel’s =PMT() function.

### Customized Quantitative Solutions for Derivative Pricing and Risk

• Excel: Theoretical exploration of option theory and Greeks for Currencies, Fixed Income, Commodities, Equities
• Excel, Bloomberg: Backtest option strategies like spreads, collars, straddles, covered calls, etc…
• Excel, IB TWS API: Link with Interactive Brokers account for trading

### Risk, Greeks

• Model for Underlying: Normal, Log-Normal
• Discounting at risk-free-rate
• Exercise: European, American
• Put, Call
• Digital, Analog
• Risk, Greeks: Delta, Gamma, Speed, Vega, Volga, Vanna, Theta, Rho (ppmu+ppr), Charm (Delta-Decay)
• Implementation in Excel, Python
• Automatically create customized price, risk, profit & loss (PnL) charts

• #### Customizable

Fully customizable to meet your needs.

• #### Implementation

Implementation in Excel, Python, Matlab

## What others say about us

Excellent and robust quantitative solutions.

QQ BirdQQ BirdQuant Bible