I originally wrote this as a twitter thread, but I thought it might be useful to send it out on substack as well. The style and flow might be a little different for that reason, but you will get the key points and I’m sure you can forgive me for the lack of literary flair you have become accustomed too.
1/ Why Bonds? Well, $BTC is a Macro asset meaning it now subject to whims of the Macro gods. One of the more influential gods residing in Macro Ásgardr happens to be Bonds. It then behooves us to understand the god of Bonds personality, what makes her tick so to speak.
2/ If you didn’t catch that: Tick size refers to the minimum price movement of a trading instrument in a market. The price movements of different trading instruments vary, with their tick sizes representing the minimum amount they can move up or down on an exchange.
3/ If you don’t know what a bond is, here is the TLDR;
A bond is an I.O.U. The borrower agrees to pay the borrower back at a certain date in the future, and make interest payments (coupons) during the life of the bond. The interest rate you are being paid is known as “yield”.
4/First let us define a bond yield (this is usually how bonds are quotes in the market.)
*Something to note, Yield is really the IRR of a bond. (Remember IRR from last week.)
5/ Ok, how do we find the yield mathematically? Here’s the idea, we need to make price equal to the present value of its future payment. (If you were paying attention over the last two week this should be familiar.)
6/ We have to suppose the bond pays a face value V at maturity T=m periods and n identical coupons a year of C/n, with its price today P. That’s a mouth full, so here is the breakdown.
7/
V = Facevalue
T = Maturity
m = compound periods (coupon paying periods)
n = identical periods
C = total amount of coupon
P = Bond price y = yield
8/ Lets break it down further. V here denotes the final payoff of the bond. n is compounding times a year, m is periods Using this discount factor we are trying to discover y (yield).
9/ Now we need to add the present value of the coupons. Each coupon is C/n which is paid from period 1 to period m, so they are discounted by 1+y/n^k.
10/ So we know P (price of bond), and we know the terms of the bond. (We can get this information online.) With this knowledge we can calculate y.
Long story short, take above formula and solve for y.
10a/ Now y is obviously random and will change tomorrow, because the price of the bond will change tomorrow. But right now we are not modeling this randomness. We are simply taking a freeze frame in time.
10b/ *Last Note: We can also get y online, just use tradingview, but we are independent and want to figure it out ourselves… right? :)
11/ Moving on, Price Yield Curve Something else to know about Bonds. Bond prices and yields are inverse. As bond price goes up, yield goes down and vice versa. So below we have price on Y axis and yield on X. As you can see price is a decreasing function of yield.
12/ The last thing I want to mention here today is the yield curve. On the Y axis I have yield and on X axis I have maturity. This can also be called term structure.
12a/ This should look familiar to options traders, however, unlike the option world where we are mapping volatility across expirations, here we are mapping yield across expirations.
12b/ You can glean a good amount of information just by looking at the curve. In fact, this is what’s being referenced when you hear the term Yield Curve Control (when the fed manipulates bond prices.)
But all that is for another time.
13/ Ok, I'm going to wrap it up, if you have question about bonds, hold them. I have two more threads to do, hopefully those will deliver some additional clarity.