Blue Horseshoe Loves This Finance Blog

  "The 'radical' of one century is the 'conservative' of the next." -Mark Twain In this series, I'm going to explore some of the advances in portfolio management, construction, and modeling since the advent of Harry Markowitz's Nobel Prize winning Modern Portfolio Theory (MPT) in 1952. MPT's mean-variance optimization approach shaped theoretical asset allocation models for decades after its introduction.  However, the theory failed to become an accepted industry practice, so we'll explore why that is and what advances have developed in recent years to address the shortcomings of the original model. The Black-Litterman Formula The Black-Litterman formula incorporates two distinct inputs; the first is the Implied Equilibrium Return Vector we constructed in Part 1, the second is a series of vectors and matrices that incorporate a manager's views/forecasts of the market.  The product of the formula is an updated Combined Expected Excess Return

  "The 'radical' of one century is the 'conservative' of the next." -Mark Twain In this series, I'm going to explore some of the advances in portfolio management, construction, and modeling since the advent of Harry Markowitz's Nobel Prize winning Modern Portfolio Theory (MPT) in 1952. MPT's mean-variance optimization approach shaped theoretical asset allocation models for decades after its introduction.  However, the theory failed to become an accepted industry practice, so we'll explore why that is and what advances have developed in recent years to address the shortcomings of the original model. The Problems with Markowitz For the purpose of illustrating the benefits of diversification in a simple two-asset portfolio, Markowitz's model was a useful tool in producing optimal weights at each level of assumed risk to create efficient portfolios.   However, in reality, investment portfolios are complex and composed of large numbers of holdin

Bringing Down the House Starting in the late 1970s, teams of blackjack players recruited from MIT began descending the Eastern Seaboard to the Mid-Atlantic casinos of Atlantic City to test a fundamental statistical principle... conditional probability. By keeping a running mental count of the number of high-value to low-value cards in a blackjack shoe relative to the size of the remaining cards in the shoe, teams could deploy dynamic betting strategies to try to take advantage of the changing probabilities of successful outcomes in the game... It worked. For the next twenty years, hundreds of Massachusetts numberphiles took on the world's casinos armed with this Bayesian principle raking in millions of dollars. Conditional Probability in Finance Conditional probability is defined as 'the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome' and it's the cornerstone of financial data modeling. Trading algorithms call indicat

     Here's a link to a presentation I gave back in August on modeling credit risk.  If anyone would like a copy of the slides, go ahead and drop me a line... https://www.gotostage.com/channel/39b3bd2dd467480a8200e7468c765143/recording/37684fe4e655449f9b473ec796241567/watch      Timeline of the presentation: Presentation Begins:                                                                0:58:00 Logistic Regression:                                                                1:02:00 Recent Trends in Probabilities of Default:                              1:10:20 Machine Learning:                                                                  1:15:00 Merton Structural Model:                                                        1:19:30 Stochastic Asset Simulation Model:                                        1:27:30 T-Year Merton Model:                

"Lighting makes no sound until it strikes." -Martin Luther King Jr. The Russell 2000 is interesting right now as the historic post-Covid run-up in small cap stocks - most notably the meme stocks of AMC and GME - has left the index in uncharted territory.... literally. This gives us a chance to explore some dynamic option valuation techniques that I've previously discussed here and in presentations to the Houston Investor's Association. Let's begin with the monthly chart... Here, we get a good look at the run small cap's have had going all the way back to 2009 but especially in the post-Covid rally.  From the context of 'variance' to the index's 20 period moving average, this period represents the most over-extended the Russell has ever been from the trailing mean. Here's the distribution of the historical 20 period variance measurements... In this chart, five of the top seven measurements are from this year... that means the upside variance f