My website is moving to **schapshow.com**, because apparently I’ve already purchased that domain. There’s probably a way to transfer it to the address I’m on right now, but I’m really not tech savvy enough to attempt that. Anyway, subscribe to **schapshow**.**com** if you’re interested. My own domain and premium theme should make the content more visually appealing and better organized. Thanks!

# Category Archives: Uncategorized

## Website is Moving!

## Fixed Income Investing at the Zero Lower Bound–Throw Away Your Fucking Finance Textbook

There’s a hopelessly confusing mess of information – some grounded in fact, some appearing on Squawk Box and similar shows – about fixed income investing in today’s macro environment. In this post, I’m not predicting the future or recommending any investment strategy, but instead explaining how and why some government securities did really well in 2014 even though pundits abound cursed them as a surefire way to lose money in 2014 . And, I should add, said pundits weren’t really all that stupid in doing so, because an oversimplified analysis of the interest rate environment pre-2014 pointed in that direction.

Rates on the U.S. 10 year treasury went down in 2014, from about 3% to 2.17%, despite widespread predictions that monetary policy would inevitably cause rates to increase. If pundits everywhere predicted this, why did the opposite materialize?

Global growth slowed down in 2014, dragging inflation down with it. Greece had another…episode, which reintroduced the possibility of a ‘Grexit’, pushing rates down further. So, by 2014’s end, the 10 year treasury rate had decreased by about 75 basis points, moving in the opposite direction from rates on high-yield debt. In other words, credit spreads widened in 2014, meaning investors demanded more compensation in order to take on credit risk (i.e. lend to corporations via bonds).

Intuitively, widening credit spreads are the result of investors demanding more compensation in exchange for lending to corporations and other risky entities, because they perceive them to be increasingly susceptible to risk in comparison to the U.S. government. Why would this be the case? Usually because the economic outlook isn’t so good – investors fear corporations are less credit-worthy due to their prospects and demand to be compensated accordingly. Furthermore, investors tend to seek the safest securities during times like these – i.e. ‘flight to quality’ occurs – namely U.S. government securities, which pushes down rates. This increases the credit spread, pushing risk free rates further away from rates on other debt.

The scenario described above is why in 2014 the average return on the 10 yr. treasury was about 10% despite the consensus forecast that they would perform poorly. Remember, the price of a bond is inversely related to the rate of interest, which is why the widening credit spread and corresponding decrease in rates pushed up the value of 10 year treasuries held by investors. To see why, think about the discount factor associated with a 10 year treasury at 3.02% versus 2.17%. In the first case (i.e. at the beginning of 2014), a $1000 par value bond is worth $741. When the applicable rate of interest falls to 2.17%, however, the corresponding price is $805.87. Clearly, the value of the 10 year US treasuries was impacted favorably by the decrease in rates, benefitting the investors who held them throughout the year. Moral of the story: interest rates are fucked up and hard to predict, and Squawk Box is almost never right.

## The Game Theory of Soccer Penalty kicks

It is reasonable to claim that when a soccer game has penalty kicks, these are one of the most important moments of the game and in that moment everyone tries to guess which side will the striker kick. Indeed penalty kicks is a type of game that game theory can solve.

To solve this game, we first need to think about the type of game, namely if it is a simultaneous game or a sequential game meaning that it is one in which the players effectively make their decisions at the same time or one in which the players take alternate turns to make their choices, respectively. In penalty kicks the players move simultaneously since the goalie cannot wait until the ball comes off the foot of the kicker to decide what to do. So, both players have to choose a side to play before the “game” starts. We will…

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## Trends in College Majors Chosen by Women

Interesting infographic courtesy of Plotly; I’m really surprised by the trend in computer science. Everything I have heard about which fields are increasingly important in our economy seemed to suggest the opposite would be the case. I’d be interested to hear some explanations.

## Indiegogo Is Testing Optional Insurance Fees For Crowdfunded Products

I’m cautiously optimistic about how this innovation could help some legitimate projects raise funds! We’ll see soon enough.

## Japan’s US$1.5 billion + United States’ US$3 billion to help developing countries leapfrog to renewables

Major news to help developing countries with the capital needed to go directly to wind and solar. By the way, the United States signed a treaty to do this back in the early 1990s, and never contributed a penny up to this point. Treaties have the force of federal law under the Constitution, don’t ya know, unless following it is something that’s optional ….

## Mathematical Statistics Lesson of the Day – Sufficient Statistics

Suppose that you collected data

$latex mathbf{X} = X_1, X_2, …, X_n$

in order to **estimate** a **parameter** $latex theta$. Let $latex f_theta(x)$ be the **probability density function (PDF)*** for $latex X_1, X_2, …, X_n$.

Let

$latex t = T(mathbf{X})$

be a **statistic** based on $latex mathbf{X}$. Let $latex g_theta(t)$ be the PDF for $latex T(X)$.

If the **conditional PDF**

$latex h_theta(mathbf{X}) = f_theta(x) div g_theta[T(mathbf{X})]$

is **independent** of $latex theta$, then $latex T(mathbf{X})$ is a **sufficient statistic** for $latex theta$. In other words,

$latex h_theta(mathbf{X}) = h(mathbf{X})$,

and $latex theta$ does not appear in $latex h(mathbf{X})$.

Intuitively, this means that $latex T(mathbf{X})$ contains everything you need to estimate $latex theta$, so knowing $latex T(mathbf{X})$ (i.e. conditioning $latex f_theta(x)$ on $latex T(mathbf{X})$) is sufficient for estimating $latex theta$.

Often, $latex T(mathbf{X})$ is a **summary statistic** of $latex X_1, X_2, …, X_n$, such as their

**sample mean****sample median****sample minimum****sample maximum**

If such a summary…

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## how to forecast an election using simulation: a case study for teaching operations research

Great post about simulating election results – I might try to adapt this to investigate how unlikely yesterday’s GOP sweep was when I get the chance. Republicans now control the Senate after winning key races in Georgia, Colorado, Iowa, and a particularly tight race in North Carolina.

After extensively blogging about the 2012 Presidential election and analytical models used to forecast the election (go here for links to some of these old posts), I decided to create a case study on Presidential election forecasting using polling data. This blog post is about this case study. I originally developed the case study for an undergraduate course on math modeling that used Palisade Decision Tools like @RISK. I retooled the spreadsheet for my undergraduate course in simulation in Spring 2014 to not rely on @RISK. All materials available in the Files tab.

The basic idea is that there are a number of mathematical models for predicting who will win the Presidential Election. The most accurate (and the most popular) use simulation to forecast the state-level outcomes based on state polls. The most sophisticated models like Nate Silver’s 538 model incorporate things such as poll biases, economic data, and momentum. I wanted to incorporate poll biases.

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## The Poisson Distribution

A Blog on Probability and Statistics

Let $latex alpha$ be a positive constant. Consider the following probability distribution:

$latex displaystyle (1) P(X=j)=frac{e^{-alpha} alpha^j}{j!} j=0,1,2,cdots$

The above distribution is said to be a Poisson distribution with parameter $latex alpha$. The Poisson distribution is usually used to model the random number of events occurring in a fixed time interval. As will be shown below, $latex E(X)=alpha$. Thus the parameter $latex alpha$ is the rate of occurrence of the random events; it indicates on average how many events occur per unit of time. Examples of random events that may be modeled by the Poisson distribution include the number of alpha particles emitted by a radioactive substance counted in a prescribed area during a fixed period of time, the number of auto accidents in a fixed period of time or the number of losses arising from a group of insureds during a policy period.

Each of the above examples can…

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## A Post on Measuring Historical Volatility

I’ve reblogged a concise yet thorough explanation of the calculation of market volatility. The post makes very clear how input parameters (weighting, time frame, etc.) affect its validity as an estimate of future market movements (link). The phrase “Fat Tails” is often thrown around like a meaningless buzzword in financial media (Squawk Box, for example), but the concept is explained intuitively here. In a separate post, market data from the S&P500 is used to demonstrate the decay factor’s effect on log returns (link).

Say we are trying to estimate risk on a stock or a portfolio of stocks. For the purpose of this discussion, let’s say we’d like to know how far up or down we might expect to see a price move in one day.

First we need to decide how to measure the upness or downness of the prices as they vary from day to day. In other words we need to define a return. For most people this would naturally be defined as a percentage return, which is given by the formula:

$latex (p_t – p_{t-1})/p_{t-1},$

where $latex p_t$ refers to the price on day $latex t$. However, there are good reasons to define a return slightly differently, namely as a log return:

$latex mbox{log}(p_t/p_{t-1})$

If you know your power series expansions, you will quickly realize there is not much difference between these two definitions for small returns- it’s only…

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