### Calculate Portfolio Performance with Modified Dietz

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

Example demonstrating how to calculate portfolio performance using the Modified Dietz method. It initializes the period, market value changes, and cash flows to compute the net performance.

```swift
typealias MD = ModifiedDietz<Double>
let df = ISO8601DateFormatter()
let beg = df.date(from: "2020-06-01T12:00:00Z")!
let mid = df.date(from: "2020-06-16T00:00:00Z")!
let end = df.date(from: "2020-06-30T12:00:00Z")!

let period = DateInterval(start: beg, end: end)
let mv = MD.MarketValueDelta(105, 100)
let cf: MD.CashflowMap = [mid: -10.0]
let md = MD(period, mv, cf)!

print("\(md.performance * 100)%")

=> 5.0%
```

--------------------------------

### Define MarketValueDelta Struct

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

Defines the MarketValueDelta struct which holds the starting and ending market values for a performance calculation period. Ensure the end value can be less than the start value.

```swift
public struct MarketValueDelta {
    public let start, end: T
    public init(start: T, end: T) {
        self.start = start
        self.end = end
    }
}
```

--------------------------------

### ModifiedDietz Initialization

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

Two initializers are provided for the ModifiedDietz type. The first is a convenient initializer with explicit parameters, and the second uses a MarketValueDelta struct and CashflowMap typealias. Both initializers can fail and return nil if invalid parameters are provided, such as a period with zero duration.

```APIDOC
## Initialization

Two initializers are provided, one more explicit than the other, but functionally equivalent:

- `init?(period: DateInterval, startValue: T, endValue: T, cashflowMap: [Date: T], epsilon: T)` - Conveniently initialize a ModifiedDietz with explicit parameters.

- `init?(DateInterval, ModifiedDietz<T>.MarketValueDelta, ModifiedDietz<T>.CashflowMap, epsilon: T)` - Initialize a ModifiedDietz with the specified parameters.

Initialization will fail and return `nil` if provided nonsense parameters, such as a period with zero duration.
```

--------------------------------

### ModifiedDietz Types

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

The library defines two key types: `MarketValueDelta` for tracking portfolio market values and `CashflowMap` for recording cash flow transactions. These types are generic and can be used with any `BinaryFloatingPoint` data type.

```APIDOC
## Types

The `MarketValueDelta` and `CashFlowMap` types are declared within `ModifiedDietz`, where `T` is your `BinaryFloatingPoint` data type:

`MarketValueDelta` specifies the beginning and ending market value for the period. Note that the `end` value can be less than the `start` value.

```swift
public struct MarketValueDelta {
    public let start, end: T
    public init(start: T, end: T) {
        self.start = start
        self.end = end
    }
}
```

`CashFlowMap` specifies the inflow (positive) or outflow (negative) of cash on particular dates. (Dates outside of period are ignored.)

```swift
typealias CashflowMap = [Date: T]
```

It's often convenient to declare your own derivative type:

```swift
typealias MD = ModifiedDietz<Float>
```
```

--------------------------------

### ModifiedDietz Properties

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

The ModifiedDietz struct exposes several computed properties that provide insights into the portfolio's performance and capital over the specified period. These properties are lazy and calculated only when first accessed.

```APIDOC
## Instance Properties and Methods

Computed properties are lazy, meaning that they are only calculated when first needed.

- `var adjustedNetCashflow: T` - Adjusted Net Cash Flow is the sum of each flow `Fi` multiplied by its weight `Wi`. Also known as total time-weighted cash flows (ttwcf)

- `var adjustedPeriod: DateInterval` - The net period excludes both (1) the time until the user funds, and (2) after the user defunds.

- `var averageCapital: T` - Average capital over the period.

- `var gainOrLoss: T` - Total gain (or loss) over period, independent of cash flow.

- `var netCashflowMap: ModifiedDietz<T>.CashflowMap` - Valid map of cash flows for period. Includes non-zero cashflows that are within `period.start < $0 <= period.end`

- `var netCashflowTotal: T` - Net external inflow (F) for the period. Also known as total net cash flows (tncf) Contributions to a portfolio are treated as positive flows while withdrawals are negative flows.

- `var orderedCashflowDates: [Date]` - Ordered list of valid cash flow dates.

- `var performance: T` - The calculated rate of return (R). Note: can return `NaN/Inf` if the sum of the starting market value and adjusted net cash flow is `0`.
```

--------------------------------

### Define CashflowMap Type Alias

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

Defines the CashflowMap type alias as a dictionary mapping Dates to a generic BinaryFloatingPoint type T. Dates outside the specified period are ignored.

```swift
typealias CashflowMap = [Date: T]
```

--------------------------------

### Declare Custom ModifiedDietz Type Alias

Source: https://github.com/openalloc/swiftmodifieddietz/blob/main/README.md

Conveniently declare a custom type alias for ModifiedDietz with a specific floating-point type, such as Float.

```swift
typealias MD = ModifiedDietz<Float>
```

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