Implied Volatility of At-The-Money Options

Note: I want to thank Algoseek for providing historical SPY option-chain data at a very reasonable price. Algoseek provides all the market data you could possibly need, including equity, future, option, forex, crypto data, and more! If you're interested in high quality market data at low quality prices, check them out here!

More …

Portfolio Construction with Risk Parity

Just like how there's more than one way to skin a cat, there's more than one way to construct a portfolio. The first systematic method of construction was Modern Portfolio Theory, put forth by Harry Markowitz. MPT's approach is simple: choose weights for each asset that maximize the amount of return received for the amount of risk or volatility taken. However, trying to maximize the risk-adjusted return of a portfolio leads to very unstable allocations, as ex-ante estimates of return are notoriously difficult and previous return isn't a good predictor of future performance.

More …

Risk Imparity: A Simple Strategy for Alpha Generation

Risk parity is a popular method of investing that aims to outperform the traditional 60/40 equity/bond portfolio by equalizing the risk of the bond portion with that of the equity part of the portfolio and then leveraging up the portfolio to hit the desired risk target. Using the covariance, and volatility of the components, we can generate a portfolio and leverage ratio for a given level of desired risk. This works for two reasons: bonds have a low or inverse correlation to equities and they generally have superior risk-adjusted returns as well, and combining low correlation assets allows us to lower the volatility of the portfolio. Bridgewater and Ray Dalio pioneered this approach in the 90s with the introduction of his now famous All Weather fund.

More …

Beta Stability: A New Persistent Factor?

The beta exposure of a stock is one of the first and most important statistics any investor looks at. Though perhaps simplistic, it distills a myriad of various properties of a stock into a single, easily digestible number. Using beta, it becomes easy to roughly forecast how an investor's portfolio would perform under different market conditions. Maybe out portfolio has a beta of 1.3 and we expect the market to return 11% next year: great, our portfolio should return around 14.3% (1.3*11%). While there's a lot of problems with this simplistic model, in this post, we're going to focus on just one: the beta of a stock changes significantly over time. Consider this graph of Apple's rolling, 252-day beta:

More …

The Value of Alternative Investments

A retail investor would be forgiven for assuming that there are really only two assets classes one should consider for personal investments: equities (stocks) and fixed income (bonds). Wherever you look, these two asset classes dominate the financial landscape. All robo-advisors and most personal advisors implement a mix of bonds and equities for the portfolios of their clients. The idea behind this mix is simple: bonds are low risk and will earn you a marginal return, while equities are riskier and will be the real engine of returns in good times. In bad times, bonds will rise, mitigating some of the losses of your equity portfolio: it's been long known and accepted that stocks and bonds have a negative correlation. Tying this strategy together is periodic rebalancing, taking money off the table during bull markets (and moving them to the safer bonds), and deploying money to the equity portion during bear markets. This in effect overlays a mean-reversion strategy onto the portfolio, boosting the returns of an otherwise static portfolio. The archetypal allocation is 60% equities, and 40% bonds, though each investor's allocation is going to differ based on his risk tolerance, age, and personal goals.

More …