Normally when folks calculate an asset’s weighted average life they use the formula $$ WAL = {{\sum_n{n \cdot Prin_n}} \over Par_0} $$ where $$ Par_n = \hbox{Par value at time n} \\[7pt] $$ and $$ Prin_n = \hbox{Principal payment at time n} \\[7pt] $$

In a previous blog post I had presented this formula $$ WAL = {\sum{Par_n} \over Par_0} \\ $$ without any context, other than to leave it to the reader to prove.

Building a Hénon map with javascript

I first found out about the Hénon map as an undergrad and have loved it ever since. Can I simulate it in javascript? Let’s find out!

The Hénon map is a dynamical system that exhibits chaotic behavior. It takes two parameters a and b. Depending on the values the map can exhibit periodic , chaotic or intermittent (switching back and forth between chaotic and stable orbits). It is described by the formula:

$$ \begin{aligned}
x_{n+1} &= 1 - ax_n^2+y_n\\ y_{n+1} &= bx_n \end{aligned}
$$

The Hénon map is basically taking the x-y plane and stretches, folds and squishes it like kneading bread. For some parameters it will tend toward a fixed point or set of points, but for others it exhibits chaotic dynamics - which means that no matter how accurately you describe the current position, it will be impossible to predict where it will be in the future (other than within the bounds of the attractor).

Back at it again Well I certainly haven’t done much with this lately. Part of that is I just feel like I didn’t have much to say and part of it is the setup I had was a little too much of a pain to deploy. Because, you know, actually having to log in and push 2 or 3 buttons is so hard. Anyway, I wanted to find a better way to host the website and figured out how to build things with AWS and GitHub.

Disclaimer First off let me say that I am by no means an authority on web technology, I wanted to re-do my website and part of that is making content. Writing non-technical things is something I’m not really great at so I’m basically forcing myself to do it here, and part of that is discussing the technologies I’ve used over the years to build it. How my websites were built The early days Back in the mid to late 90s, around the time I was graduating from college, the web started to become a thing.

Tiktok shortcode for Hugo When i was trying to post my adorable Tiktok of a wee baby duck that was just hatching, I couldn’t find anything about embedding Tiktoks into Hugo. I tried just pasting the embed code into a markdown page, but it didn’t work so I wrote a quick and dirty shortcode to do it: tiktok.html: Save this code in \layouts\shortcodes\tiktok.html <script async src="https://www.tiktok.com/embed.js"></script> <blockquote class="tiktok-embed" cite="https://www.tiktok.com/{{ .Get "usr" }}/video/{{ .

Please enjoy this Tiktok of a baby duck hatching =)

@chaos46692

Music

A while ago for work I had created a process that required a formula for the weighted average life (WAL) of a mortgage with level payments. I found one online:

$$ W = N D_N - \frac{1}{r} $$

where:

$$ \begin{aligned}
d &= { 1 \over 1 + r} = \hbox{one month discount factor} \\[7pt] r &= {a \over 12} = \hbox{monthly discount} \\[10pt] N &= \hbox{Loan period in months} \\[10pt] D_n &= {1 \over 1-d^n} \end{aligned}
$$

That formula is pretty convenient because it means given a rate and a WAL we can solve pretty easily for how long the loan has to be in order to have a particular WAL without doing a bunch of infinite sums. So where does that fomula come from? Originally I found it here , but I wanted to see if I could derive it.

I’ve had a lot of fun setting up Hugo to set it up how I want. I will caveat this with a few things - I tried to do things the right way but often times, but I’m pretty new at this so more than likely I’ve made some beginner’s mistakes along the way. Also note that at the original writing of this I was using a host, but have moved since then to hosting on AWS.

While setting up this website I was constantly greeted by this in my address bar: I have no real reason for it to bother me, but it surely did. This must be remedied. My hosting is different from my registrar/DNS so accomplishing it took a little more work than it might if you have all that stuff in one place. I use namecheap as my registrar/DNS and HostPapa for my hosting (mostly because I used to use Lunarpages and they got bought by HostPapa).

Well hey look it worked! That’s pretty rad. I don’t have a lot to add to this, mostly this post is to make sure the script that I wrote to autobuild and commit to [GitHub](git commit -a –allow-empty-message) works =)