CashflowAnalysis.jl

### A Pluto.jl notebook ###
# v0.20.8

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    return quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
    #! format: on
end

# ╔═╡ 228bfdfe-0d40-11eb-1dbb-4f01ce119bb1
# the packages used in this notebook:
begin
	using FinanceModels
	using ActuaryUtilities
	using Plots
	using PlutoUI
end

# ╔═╡ 641950d0-0d44-11eb-260c-ed92def0b60a
md"# Cashflow Analysis with ActuaryUtilities"

# ╔═╡ 8a5d9f90-0d48-11eb-1be6-8d6836ff1dbe
md" 
This notebook has two examples of cashflow analysis:

1. Bond pricing, duration, and convexity
2. Investment anaylsis that contrasts two projects' IRRs and breakeven time points
"

# ╔═╡ cc0232a0-0d46-11eb-06a6-8d7fa5c047ef
md"## Example 1: Bond metrics"

# ╔═╡ 8deba520-0d44-11eb-3dab-ab18e69d2dde
md"**Bond Maturity Time:** $(@bind maturity Slider(1:30,
show_value=true,
default=20
))"

# ╔═╡ 68c87dd0-0d40-11eb-16bf-8ff874bc3ea3
md"**Bond Yield To Maturity (Bond Equivalent Yield):** $(@bind yield_to_maturity_rate Slider(0.01:0.005:0.25,
show_value=true,
default=0.12
))"

# ╔═╡ 9cd700f2-c289-406b-84d5-f3b5ff940596
yield_to_maturity= Periodic(2)(yield_to_maturity_rate)

# ╔═╡ 8a005e00-0d40-11eb-09b4-8b555c921337
par = 100

# ╔═╡ 32705820-0d45-11eb-2582-e75cd402b760
md"First, let's create some cashflows to analyze by constructing a semi-annual coupon bond: with $par par"

# ╔═╡ 68b096c0-0d45-11eb-2a97-293edb087ded
times = [t for t in 0.5:0.5:maturity]

# ╔═╡ 4924d230-0d40-11eb-1485-4f320034b132
bond_cfs = map(times) do t
	if t == maturity
		par * (1 + rate(yield_to_maturity) / 2)
	else
		par * rate(yield_to_maturity) / 2 
	end
end


# ╔═╡ 4539f4b0-0d46-11eb-1976-e7a12682c958
md"There are a number of functions for common metrics:"

# ╔═╡ 6803336f-8842-4531-bac3-06e6897d0852
duration(yield_to_maturity, bond_cfs, times)

# ╔═╡ 3d9aa81b-9426-4e7d-aa82-dbd14582c71a
original_price = present_value(yield_to_maturity, bond_cfs, times)

# ╔═╡ 75bd8030-0d45-11eb-1546-3b5e18fb4144
let 
	y = yield_to_maturity
	(
		PV        = present_value(       y, bond_cfs, times),
		Duration  = duration(            y, bond_cfs, times),
		Macaulay  = duration(Macaulay(), y, bond_cfs, times),
		DV01      = duration(DV01(),     y, bond_cfs, times),
		Convexity = convexity(           y, bond_cfs, times),
	)
end

# ╔═╡ 42d85ace-0d42-11eb-1814-97ae8f46a2f8
md"**Discount rate:** $(@bind disc_rate Slider(0.01:0.005:0.15,show_value=true,default=0.05))"

# ╔═╡ 3d2c97a0-0d41-11eb-31b3-67ce8f27c211
begin
	scatter(
		times,
		bond_cfs,
		legend=:topleft,
		ylim=(0,maximum(bond_cfs)*1.05),
		xlim=(0,maturity * 1.05),
		xlabel=time,
		label="Bond Cashflows",
		title="Bond cashflows and durations: $(disc_rate*100)% discount",
		marker=(:grey, 5, 0.7),
		markerstroke=0,
	)
	vline!(
		[duration(disc_rate,bond_cfs,times)],
		label="Duration",
		line=(:blue,4,0.5)
	)
	vline!(
		[duration(Macaulay(),disc_rate,bond_cfs,times)],
		label="Macaulay Duration",
		line=(:purple,4,0.5)
	)
	vline!(
		[duration(DV01(),disc_rate,bond_cfs,times)],
		label="DV01",
		line=(:orange,4,0.5)
	)
end

# ╔═╡ 8cfcbc08-84b0-4f6c-83c2-fc9e225bee4d
md"""
### Book and Market Yield

In the above example, the bond was priced at a market=book yield of $yield_to_maturity_rate.

However, what happens to the yield if the value were to change from when you purchased the bond at $(round(original_price;digits=2))?

**New market value of bond:** $(@bind new_bond_mv Slider(round(Int,original_price*0.5):round(Int,original_price*2),show_value=true,default=round(Int,original_price)))
"""

# ╔═╡ c3e46e0c-d3a3-43a7-9756-b7f4f0f2b527
plot(0.01:0.01:0.15,y->duration(y,bond_cfs,times))

# ╔═╡ f9938710-ac4d-43be-868a-23ffd43b6772
returns = (
	book = irr([-original_price; bond_cfs],[0;times]),
	market_yield = irr([-new_bond_mv;bond_cfs],[0;times])
)

# ╔═╡ 8f535775-1e8e-4bb5-92a2-e0680114c986
# estimate the market yield from the duration and convexity
let 
	b = returns.book 
	d = duration(yield_to_maturity, bond_cfs, times)
	c = convexity(yield_to_maturity, bond_cfs, times)
	Δp = (1 - new_bond_mv / original_price)
	first_order_change = Δp / d
	second_order_change = (√(2 * c * Δp + d^2) + d) / c
	second_order_change2 = (d - √(2 * c * Δp + d^2)) / c

	
	# estimate with convexity needs to be corected
	(b + first_order_change,b - second_order_change2)
end

# ╔═╡ beff1218-68e3-4b82-9bac-d47b87bbcbf6


# ╔═╡ fe2288c0-0d46-11eb-3195-3bb968cba644
md"## Example 2: Investment Cashflows"

# ╔═╡ 0e8d432e-0d47-11eb-3eb0-ffd26ebdbd0e
project_A = [-10,4,3,3,2,1,1]

# ╔═╡ 2bb71532-0d47-11eb-1bf8-59387e9c40a5
project_B = [-20,5,5,5,5,5]

# ╔═╡ 388a29ee-0d47-11eb-10dc-6fc8ee792c5e
let
	p1 = bar(project_A,title="Project A CFs",ylim=(-25,10),legend=false)
	p2 = bar(project_B,title="Project B CFs",ylim=(-25,10),legend=false)
	plot(p1,p2)
end
	

# ╔═╡ e69b7940-0d47-11eb-13a4-7f437899aafa
(
	IRR_A = irr(project_A),
	IRR_B = irr(project_B),
	)

# ╔═╡ 70aa2fa0-0d48-11eb-00b9-114c73cc50ee
md"The time until the project breaks even with a borrowing cost of 5%:"

# ╔═╡ 0badd480-0d48-11eb-3e85-cfecde9d1ad5
(
	breakeven_A = breakeven(     0.05, project_A),
	PV_A  = present_value( 0.05, project_A),
	breakeven_B = breakeven(     0.05, project_B),
	PV_B  = present_value( 0.05, project_B),
)

# ╔═╡ c98e6190-0d48-11eb-17fb-a9413b985194
md"
### Term structure of rates with *FinanceModels.jl*

The yield used doesn't have to be a flat rate. You can use a term structure of rates. Using the project cashflows from above, here's the present value and duration: 
"

# ╔═╡ 3ba513a0-0d49-11eb-39e9-a7728113dfec
curve = let 	
	spot_rates = [0.06, 0.08,0.0975,0.1085,0.1145,0.1168,0.1178,0.1187,0.1187]
	maturities = 1:9
	quotes = ZCBYield.(spot_rates,maturities)
	fit(Spline.Linear(),quotes,Fit.Bootstrap())
end

# ╔═╡ e0717370-0d48-11eb-3629-d32dbb85b749
present_value(curve,project_A)

# ╔═╡ c6333330-0d49-11eb-2b1c-51c85729ba28
md"The duration of the inflows after the initial investment:"

# ╔═╡ e0495c90-0d49-11eb-2fc7-63826c1830c7
duration(curve, project_A[2:end], [1,2,3,4,5,6]) # the last vector is the timepoints

# ╔═╡ 23dfe9b0-0d4a-11eb-2030-5ba3bbf9519e
md"## Extras"

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git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "c950ae0a3577aec97bfccf3381f66666bc416729"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.8.1+0"
"""

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