Get Paid to Take Risk

Is the risk-reward trade-off broken? Historically smaller companies have higher stock price returns, but this relationship has faded since 2008. What happened and why aren’t investors being compensated for taking more risk?

Table 1.1 shows how small cap stocks have performed relative to large cap stocks since the Great Financial Crisis in 2007-08. There is more volatility associated with small caps, but only a small amount of return compensation. What’s going on? For contrast, I provide the same metrics before the GFC in Table 1.2 and Chart 1.2 below.

Table 1.1: Small vs Large Cap Since the Great Financial Crisis (GFC)


Small cap barely outperforms, and has more volatility (measured by standard deviation of stock returns). This reinforces the risk-reward dynamic. Chart 1.1 below shows this graphically. Note: SPY is the S&P 500 Index ETF (Large Cap proxy); IWM is the iShares Russell 2000 Index ETF (Small Cap proxy).

Chart 1.1: Small vs Large Cap Since the GFC


Table 1.2: Small vs Large Cap Pre-GFC


Over this time period, small cap outperforms significantly with the same difference in volatility. You were rewarded more for taking risk in the pre-crisis era. Chart 1.2 below shows this graphically.

Chart 1.2: Small vs Large Cap Pre-GFC


So what gives?

Why aren’t investors being rewarded as they were before the GFC in 2008?

The answer boils down to how companies raise money. When a firm is going to undertake a new project (called capital budgeting in the biz), top brass has to decide whether to sell bonds to raise cash or to give up portions of their company (called equity) to raise cash. In order to do this, they need to weigh their options, so to speak.

Companies can minimize their cost of raising cash (called the cost of capital) by optimizing the following equation with respect to the weights of equity and debt.

Table 2.1:


Cost of equity = f(company size, business risk, reputation)

It should be noted that if a company goes bankrupt, they have no obligation to pay their shareholders anything. Period. The investor accepts the risk that his investment may go to zero in exchange for a bit more return. Investors in stock take risk and are paid in stock returns or dividends. Because of this, cost of equity is always greater than the cost of debt.

Cost of Debt = f(credit conditions, company size, debt outstanding, business risk)

Debt holders are the first to be paid back should a company default. In exchange for this assurance, the company gets to borrow at a lower rate. Lenders, or buyers of the debt, receive less in return. Less risk, less reward.

In the case of both debt and equity, long established companies, like IBM or Exxon Mobil, will have a lower cost of raising capital than a recently established tech start-up. This can also be called the Size Premium. This is why you should be compensated more for owning a small company’s debt or equity.

Large Scale Asset Purchases aka Quantitative Easing:

Chart 2.1: Treasurys and Mortgage Backed Securities owned by the Fed


When financial markets began to fail in 2008, the Federal Reserve of the United States stepped in and started buying up mortgage backed securities (MBS) and US Treasury Bonds in order to stimulate the economy by artificially lowering interest rates to allow easier borrowing for companies. Cheaper debt means more companies can borrow to finance new projects, growing consumption of capital goods; at least that was the plan.

They did this in several stages known as QE1, QE2, & QE3. Some were even forced to borrow cash from the Fed in order to send a signal of stability.

Borrowing from the [Fed], even on a confidential basis, has long been viewed as a sign of weakness, to be avoided if at all possible. … [The Fed] arranged for four of the nation’s largest banks — Bank of America, Citigroup, JPMorgan Chase and Wachovia — to take what were described as symbolic loans of $500 million each. (Sauce)

Lion’s Share

Where did this liquidity go? Big banks lent it out to the nation’s largest institutions, doing what they do best, making money. They borrowed from the Fed at wicked cheap levels and lent to corporations at a higher rate which were still well below historic borrowing rates. Everyone wins, right? But who were the biggest winners?

The amount of debt a bank is willing to lend a company is directly related to the size of their operations. The bigger the firm, the more they can borrow. So who got the lion’s share of the injected cash? Big business. Think Apple, Microsoft, Amazon, Berkshire Hathaway, Facebook, JP Morgan, Johnson & Johnson, Google, Exxon Mobil, Bank of America, Visa, etc.

In order to lower their cost of capital (WACC), companies took out debt, which was now the cheapest it’s ever been since at least 1962 (see Chart 2.1). But instead of financing investments in brick and mortar or research and development, they used it to purchase their own stocks.

This shifted the weights of debt and equity.

Returning to the Cost of Capital Equation:


  1. Cost of debt falls.
  2. Companies raise more debt.
  3. They use the debt to purchase equity
  4. Lower Cost of Capital

Chart 2.1: US Treasury 10-Year Yield since 1962


Through stock buybacks, companies were literally purchasing their own stocks to lower their weight of equity. The more stock they purchase, the more their stock prices rise. This brings me to the punchline: large caps are performing the same as small caps because of Quantitative Easing. This isn’t guess work, it’s exactly what’s happening in  financial markets worldwide. Until interest rates behave as they did in pre-crisis, pre-QE times, I don’t expect small caps on average to perform much better than large caps given the elevated level of risks.

Further, “the top 1 percent of Americans control 50 percent of the financial wealth, [thus] they gain the most when these asset prices boom” (Sharma, p. 108). In 2014, The Fed issued a statement, “our goal is to help Main Street, not Wall Street” (WashingtonPost), yet the Fed has been feeding inequality since. I don’t mean to be critical, but the Fed has to have realized that it had this effect.

Don't pretend to be something you're not.

I think the Fed did the best with what it had. When all you have is a hammer, everything looks like a nail. They saved many in the aftermath of the crisis, which I believe would have been much deeper without Federal Reserve intervention.

Bottom Line (TL;DR):

I’m long large cap, high dividend stocks, for reasons stated in this article, as well as the tendency for high dividend stocks to outperform in rising interest rate environments. Here’s the source for that last statement: GlobalXFunds.

Thanks for reading, this was a fun one to write.



  1. NYT: The Fed’s Crisis Lending, Mar. 31, 2011.
  2. Sharma, Ruchir. The Rise and Fall of Nations. 2016.
  3. FRED
  4. Bloomberg

Knee Jerk Vol & the Fed


The Fed is now shrinking its balance sheet; they are no longer buying new securities as they mature. Below is a bit of analysis on if the Fed’s recent activities in shrinking its balance sheet is the cause of the recent rise in volatility.

Quick note: Data is at a weekly tenor, from Jan. 8, 2014 to April 4, 2018.


The thinner vertical line denotes when the Fed began to shrink their balance sheet last October; the thicker vertical line denotes when we had that massive vol spike in February of this year.

On the surface, the Fed’s action doesn’t appear to be the cause of all the hullabaloo, i.e. the shift from risky assets to safer assets.

If we turn to bonds, we see the following.


Rates on 10-Year Treasurys have moved higher since the Fed began shrinking it’s holdings of US Treasurys. Recall, bond prices fall as rates rise. Less buyers = lower prices = higher rates.

It appears these movements aren’t directly related to the recent rise in volatility.

However, there appears to be an inverse relationship between bond rates and the VIX Index.

A simple linear regression would see if the markets follow each other and if there was any preditcability between the markets. The equation is as follows:


Regression Summary:

reg summary apr6.JPG

We see a significant coefficient, with a value of -8.545, and an insignificant alpha. Therefore your new equations is:


If you predict a 25 bps rise in bond rates, we would expect to see a 2.3136% fall in the VIX Index, with 95% confidence:


The VIX is crazy volitile and the regression has a small R squared, so take the results with a grain of salt.


Thanks for reading,



  4. Yahoo Finance
  5. Bloomberg


Note: The VIX and the 10-Yr are already percentages, so they’re calculated in absolute terms.

Delta VIX = VIX Value Today – VIX Value Yesterday

Delta 10-Yr = 10-Yr Today – 10-Yr Yesterday

Bogus Tweet Risk


Most financial media is focused on “tweet risk” or “trade wars”. To me, these seem like water under the bridge. It’s in China’s interest politically to retaliate to trade sanctions, but not in their interest to crash US markets. They hold a massive amount of US Treasurys, if they stop buying US bonds, rates will shoot through the roof and China loses. The following analysis attempts to succinctly summize the economic situation.

Tempered Expectations of Future Growth

We’ve crossed the 50 bps level in the 2 to 10 year US Treasury Spread, signaling lower expecations of future growth prospects, strengthening the late stage economic growth narrative.



US Dollar Slides


The DXY Index represents the US Dollar vs a basket of major currencies. Yields in the above chart are represented by the Generic 10-Year US Treasury yield. Higher yields depreciate a currency, as stated by Interest Rate Parity.

A weaker dollar allows foreign investors more buying power in US markets.

Resilience of US Goverment Capital Markets

The 10-Year Treasury rate now sits at around 2.75% following last week’s sale of a LOT of Treasurys. The market is handling this flood of supply well (nearly $300bil last week), as bonds have rallied in the face of rising interest rates. The US Treasury Department will auction off $48bil of 3-month T-bills and $42bil of 6-month T-bills this week.

Rates on the short end are slightly higher following a Fed funds rate hike in March, but longer term yields have fallen since last month signaling strong demand for US debt.


Higher Volatility but Lower Tail Risk

We’ve seen elevated levels of stock market volatility since the beginning of the year. However, since last month we’ve seen less tail risk, i.e. a flatter Volatility Skew.

  1. Elevated levels of Volatility overall
  2. Lower levels of Vol Skew


Tail Risk is the risk of a Black Swan event. This is measured by the relative demand of out of the money calls and puts. As the volatility smile flattens, the market is pricing in less tail risk, albeit at an elevated level of overall volatility.

Higher vol means more trading, which is good for financial services, as are higher rates. A trade war will be bad for industrials. I’ll be watching financials (XLF), and industrials (XLI).

Thanks for reading,


What I’m Reading: Lords of Finance: Bankers Who Broke the World




Disclaimer: The opinions above are my own and are for information purposes only.  This post is not intended to be investment advice.  Seek a duly licensed professional for investment advice.


Predicting the Future…

Autocorrelation occurs where past data can be used to predict the future. *snore*. If you’re still reading, think about it like this. If you know your friend, Alex, is always late, you will assume that he will arrive late every time. But if Alex is only late some of the time, you’re not sure when he will actually arrive on time, or when he will be late. We can observe what’s happening or use an ARCH test. Hang with me here.

Let’s say Alex is involved in an afterwork softball team, and they play on Tuesdays and Thursday. Games tend to run longer than scheduled. You notice that he only late on Tuesdays and Thursdays; you can start to predict his tardiness. So if your buddy wants to get beers on a Tuesday after softball, you can expect him to be late. You’re using past data to predict the future.

If I had used an ARCH model to predict when my buddy would be late, it would have told me that on average, my friend is late on Tuesdays and Thursdays more than any other days.

Maybe I missed my mark here, but the idea is not simple. If you need further clarification here’s the investopedia version:


The goal of the ARCH test is to control for autocorrelation in variances, then see if there is any kind of pattern there. Control for the mean, then look for a pattern in the errors. If there’s a pattern in the variances, and we can predict when the next period of high variance will be. You’ll be predicting big booms and drops. Timing the market would be possible, and also arbitrage opportunities more easily identifiable (which is what hedge funds do).

ARCH outline:
First log returns to make your data symmetrical. To get rid of autocorrelation in the variances you use a “lagged time factor” of volatility. The ARCH and GARCH models control for a stationary mean in the variances. Like this, using σ for variances in returns:


If you look at the equation above, you’ll see that we want a βvalue of 1 in order to prove that past volatility is a predictor of volitility. If β1 doesn’t equal 1, that means all currently accepted limits of risk are bogus.

Investors use these tests to forecast how volatile markets will be in the future. All current models of risk used at big banks all over the country assume volatility is random and normally distributed and that it can’t be predicted. Volatility rises and falls randomly, following a random path according to these models (Monte Carlo, Analytical).

Lehman blew up at the end of 2008 because it was using Monte Carlo simulations to predict how much the bank could lose on any given day. This model assumes normal behavior; i.e. normal returns, normal variance. In times of panic, the market’s behavior is far from random. The ability to predict when these times of high volatility will be remains allusive to companies and investors alike.

There are also some implications in proving how inefficient (unfair) options prices are. If you can prove that future options premiums are over- or underpriced, there’s an opportunity to make money.

My professor, Mr. Asensio, used the analogy of charging someone for “falling tree insurance”. The insurance company will give you a quote; say $2,000 dollars a year to cover your house if a tree falls on it. Say the average damage cost for a homeowner is $40,000 every time a tree falls into their home. The insurance company is expecting a tree to fall on your house once ever twenty years. If you pay $2,000 a year for 20 years and in the 20th year a tree falls on your house, you broke even. You got out ($40,000) what you paid in ($2,000*20). (Assuming the exact cost to fix your house was $40,000).


A futures contract is an agreement to purchase an asset at a set price at a future date. For example, if I’m going to sell you my car and you can’t pay me until next month, but I agree to sell you the car at the agreed price next month. We’ve just entered a futures contract.

Further, suppose your car was an expensive, one-of-a-kind Ferarri; custom-built for you. One of one. After you agree on a set price, news comes out that they’re building 500,000 more Ferarris just like yours. The price for your Ferarri is going to drop because it’s no longer the only one of its kind.

But who cares, I’ve already locked in the price and my buyer is still on the hook to pay me the full amount.

Again, using the Ferarri example, say before he buys, the buyer hears rumors that Ferarri was going to start producing the model of your Ferrari again. He expects the price to go down, but he still isn’t sure how much the price will fall, because Ferarri has yet to announce how many new cars they will produce. He wouldn’t buy the Ferarri at today’s price, he would negotiate for a lower price; guessing how far it will drop when Ferarri announces their increase in production. He is essentially forecasting the price drop when the news is announced.

For instance, the buyer assumes that there will be 500,000 more Ferraris made. He makes his views known in the negotiation process, but the seller disagrees. The seller thinks they’re only going to make 250,000 more. They hammer out a deal, each weighing their risks if the other party’s predictions are correct. They arrive to an estimate somewhere in the middle, say 375,000 and price the car accordingly, each happy they got a deal.

The buyer is happy because he is purchasing a Ferarri at less than market price. The seller is happy because he knows the price of the Ferarri could drop much lower than the agreed upon price.

The problem with this occurs when one party’s predictions are correct a higher percentage of the time, and the price on the futures contract doesn’t take that into account.

Bob from Big Bank of America is a seller of futures contracts. He understands markets very well, and is able to predict futures prices better than you (the buyer). You think you think your prediction is just as likely to be correct as his, so you hammer out a deal somewhere close to the middle of your two estimates. He is getting the better deal, because his estimate of the prices is always closer, but he can negotiate for a better deal.

Assume per gallon price of gas is $2.50 today. Bob says he will sell me gas for $2.25 a gallon, but I can’t have it until tomorrow. Bob expects the price to drop to $2.00 tomorrow. Playing the ignorant investor, I think buying gas for $2.25 a gallon is a steal. So I take his deal and tomorrow the price actually drops to $2.10 a gallon, I get caught with my pants down, because I’m stuck overpaying for gas today. Bob gets a great deal, because, although he was wrong about the drop, he still sold the gas at higher than market price.

The ARCH test tries to find when Big Bank Bob is hustling markets. They try to find where one party is better at predicting the price over the other. As an investor you want to put your money on the party that is usually right. You can make big money on these using levered bets. Risky? Yeah. Dangerous? Maybe. Potentially Lucrative? Absolutely.

I hope I increased your understanding of futures markets and how these things are calculated.

– Tommander-in-Chief


Disclaimer: If markets are efficient, you can’t make money here. If insurance companies are paying out exactly how much they charge for their products, they don’t make money. The insurance is appropriately priced, and neither party would engage in any type of transaction. But people buy insurance on everything from houses, to boats, to teeth. They think that by paying a small amount each month, they can avoid being slammed at by a big bill. Buyers of insurance certainly think they are getting a good deal. If insurance companies achieve a steady stream of cash flows and predictable payouts, they can generate profits by charging a tiny premium on your insurance over the predicted value. Essentially this tiny premium is a “peace-of-mind premium”; so you can sleep at night not worrying about if the tree in your front yard goes through your living room window you’ll be slapped with a big bill. All in all, insurance are arranged so both parties gain.