Tag: Navy (Page 3 of 58)

Finance Friday: Horizon Tech (HRZN), A Dividend Workhorse

One of the goals of my input to our stock portfolio is to have sufficient cash flow from interest and dividends alone to support my wife when I punch out. I use this term not as in an injection from an aircraft, but as leaving life as it’s known on earth. Recently, I went to work, rationalizing several stocks and reinvesting them in HRZN, which currently has an over 20% return. This blog takes you through how I checked HRZN out before pushing the go button on the investment, which currently stands at 3000 shares.

Our broker, Schwab, offers many research-oriented pathways. This is the first area I explored upon the start of my initial due diligence. One such report on HRZN in PDF format is presented below for information. I gleaned from this type of info that, in general, the purchase of HRZN was not recommended, but being a contrarian, I noted that the price appeared to be bottoming out. This, in and of itself, presents an opportunity. I also observed that HRZN was a consistent payer of its monthly dividend, without any reductions. To me, this was an opportunity to buy at or near the dip and maximize potential returns.

I then turned to Perplexity.ai with numerous prompts.

I am attempting to maximize short-term dividend returns. Would you buy HRZN, all risks aside

Suppose the sole objective is to maximize dividend return in the short term, and all risks are ignored. In that case, HRZN is an unusually strong candidate based on its current forward yield (about 20% at $0.11/month and ~$6.68/share) and its consistent history of monthly payouts. This high yield is well above that of most dividend stocks or funds, and monthly compounding via DRIP further enhances short-term income.

However, such high yields are rarely sustainable and often signal underlying risk, such as the potential for dividend cuts, portfolio losses, or share price erosion. But with risk disregarded, HRZN offers unusually rapid dividend accumulation and cash yield, making it one of the best vehicles for short-term dividend maximization among widely available equities.

I am OK with the risks involved, having owned HRZN several times previously and having bought 3000 shares at various prices, as low as $6.44. Given the investment of slightly over $18,000, I then turned back to Perplexity with additional queries. One is shown in the PDF below:

At the point I had accumulated 1000 shares, I did another query about accumulation as shown in the PDF below;

Of interest to me is how long it will take my investment to double? See PDf below.

I invested most of my money in HRZN before its ex-dividend date in November, so I should receive the first dividend payment shortly. The price has eroded somewhat to the point I’m currently down a couple of grand, but ups and downs are part of the game. I am in this for dividends, which are independent of price fluctuations once purchased.

The History Behind ‘Dance With Me, Henry’

As a fifteen-year-old in 1955, a song titled “The Wallflower” started playing on the radio. Soon, a title “Roll With Me Henry” was announced, followed by “Dance With Me Henry.” Predating these renditions was an often-banned song by The Midnighters named “Work With Me Annie.” The two had similar sounds and messages. I’ve embedded the original version below, followed by Perplexity’s take on what was happening in the original song. Keep in mind that my first name is Henry, so I had more than a passing interest in this song at 15.

“Dance With Me Henry” is a song originally recorded in 1955 by Etta James and her vocal group, The Peaches, under the title “The Wallflower (Roll With Me Henry)”. The song was written by Etta James, Johnny Otis, and Hank Ballard as a response—a so-called “answer song”—to Ballard’s earlier hit “Work With Me Annie”. The name “Henry” in the lyrics is not a specific person but rather a stand-in for a male dance partner. The song uses playful call-and-response and flirtatious lyrics, which, for the time, were considered suggestive.wikipedia+6

Song Origins and History

  • The original was recorded by Etta James and The Peaches, with uncredited responses by R&B singer Richard Berry.udiscovermusic
  • It was released on Modern Records and became a No. 1 R&B hit for several weeks in 1955.udiscovermusic
  • The song’s bold sexual innuendo led to its title being changed from “Roll With Me Henry” to “The Wallflower” to avoid FCC censorship.culturesonar+2

Covers and Popularity

  • Pop singer Georgia Gibbs covered the track as “Dance With Me Henry” (sometimes listed as “Dance With Me Henry (Wallflower)”), sanitizing the lyrics for the pop market.facebook+1
  • Gibbs’ cover became a No. 1 hit on the mainstream charts, eclipsing James’ original in crossover reach. youtube​facebook
  • Etta James later covered the pop version herself.culturesonar

Musical Style and Legacy

  • The song bridged blues, gospel, and early rock and roll, influencing later artists and genres.culturesonar+1
  • James’s assertive vocals signaled a breakthrough for female empowerment in R&B and rock.culturesonar
  • It was later featured in the movie “Back to the Future” and inducted into the Grammy Hall of Fame in 2008.udiscovermusic+1

The “Henry” Character

  • “Henry” is not a real person but represents the desired male partner—or foil—addressed by the narrator in call-and-response fashion.songfacts+2
  • In the original, Richard Berry plays Henry in vocal interchanges with James.udiscovermusic

Groups and Notable Artists

  • Original: Etta James and The Peaches (with Richard Berry responding as Henry).udiscovermusic
  • Songwriters: Etta James, Johnny Otis, Hank Ballard.backtothefuture.fandom+2
  • Notable cover: Georgia Gibbs on Mercury Records.youtube​facebook

The song’s story is a classic example of how rhythm & blues tracks crossed over to pop audiences—with altered lyrics and broader appeal—while the originals often paved the way for significant musical and cultural shifts.culturesonar+1

  1. https://en.wikipedia.org/wiki/The_Wallflower_(Dance_with_Me,_Henry)
  2. https://www.culturesonar.com/etta-james-and-roll-with-me-henry/
  3. https://www.facebook.com/groups/DoYouRememberThe60sFanClub/posts/2226004974458790/
  4. https://www.udiscovermusic.com/stories/etta-james-the-wallflower-song/
  5. https://backtothefuture.fandom.com/wiki/The_Wallflower_(Dance_with_Me,_Henry)
  6. https://www.youtube.com/watch?v=xSJTWUo-WWQ
  7. https://www.britannica.com/topic/The-Wallflower
  8. https://www.facebook.com/groups/824194430969202/posts/9367835869938306/
  9. https://www.facebook.com/groups/824194430969202/posts/on-june-23-1955-we-were-hearing-dance-with-me-henry-by-georgia-gibbs-sanitizing/9848441101877778/
  10. https://www.reddit.com/r/78rpm/comments/1osh51e/ronnie_stevens_dance_with_me_henry_jack_arthur/
  11. https://www.songfacts.com/lyrics/etta-james/the-wallflower
  12. https://open.spotify.com/track/5neyzFjnykdFbcmMmTGSzZ
  13. https://en.wikipedia.org/wiki/Dance_with_Me,_Henry
  14. https://www.youtube.com/watch?v=Ta5400IjRQA

Understanding Viral Warts in ESRD Patients

Today, I’m going to provide more information on something I am experiencing, Viral Warts. Tomorrow I have a real go-around with my new dermatologist, where we should start to have some of the numerous cancers on and around my head treated. If I’m still alive (grin), I will relate the experience. Friday, I have, IMHO, a really great Financial Friday in mind for you. As in the past, it will be based on my actual investment activity, how I decided what to invest in, and what the investment’s future may yield. Wednesday and Thursday are open at this point, and on Sunday, when I’m writing this blog. I just picked up on the Grammarly AI writing assistant with Black Friday half-price deal, so standby.

During last week’s meeting with my dialysis team, we (my wife and I) brought up the subject of Viral Warts and didn’t get anywhere or any satisfaction. We don’t know if they had not encountered them previously or if it was just a lack of empathy. At times, they can be stoic at best, probably hardened by their experiences, which is understandable to a degree.

So, aside from being diagnosed with this new affliction, I wanted to know more about the population of dialysis patients “blessed” with viral warts. I turned to Perplexity.ai with the following prompt and results. Along the way in researching this topic, I learned that I fit just about all of the If then -> warts criteria: age, sex, time on dialysis, etc.

Prompt: What are the characteristics of ESRD patients who develop renal warts?

Most descriptions of “who gets warts” in kidney disease are about transplant recipients, so the data for ESRD itself are thinner; however, a pattern emerges from dialysis and CKD skin‑series and from HPV‑cancer data. In ESRD, warts seem to occur in patients who share the general ESRD risk profile (uremic immune dysfunction, long disease duration) plus the usual HPV risk factors seen in the general population.pmc.ncbi.nlm.nih+3

Demographic tendencies

  • Middle‑aged and older adults: HPV‑related cancers in ESRD peak around ages 50–64, implying that persistent HPV infection (and thus warts) is most relevant in this age band.pmc.ncbi.nlm.nih
  • Both sexes are affected, with some signals by sex: For HPV‑related cancers in ESRD, female sex is a risk factor (IRR ≈ 2.1 vs ESRD men). For cutaneous warts specifically, one CKD skin‑disease review notes common warts among ESRD patients without a strong sex skew. Still, detailed sex‑stratified wart data are rarely reported.pmc.ncbi.nlm.nih+2

Renal and dialysis‑related characteristics

  • Advanced, long‑standing renal failure: Reviews of cutaneous disease in CKD/ESRD emphasize that viral infections including common warts are a recognized problem mainly in patients with advanced uremia and on long‑term renal replacement therapy.actasdermo+1
  • Dialysis, any modality: Hemodialysis cohorts show low but definite wart prevalence (a few percent in series of 100–200 patients), and authors note that “human papillomavirus–induced warts are common in kidney disease,” reflecting the background uremic immune defect rather than a specific dialysis type. Peritoneal dialysis appears similar or slightly less studied rather than clearly different.pmc.ncbi.nlm.nih+1
  • Heavy comorbidity burden: ESRD patients with higher overall comorbidity have more infection‑related complications in general. However, for HPV‑related cancers specifically, comorbidity level was not a clear additional risk factor once ESRD status itself was accounted for.karger+1

Immune and virologic factors

  • Uremic immune dysfunction: Reviews of skin disease in CKD highlight that ESRD patients have impaired cellular immunity, altered T‑cell and antigen‑presenting cell function, and chronic inflammation, which collectively predispose to chronic viral skin infections such as warts.actasdermo+2
  • Difficulty clearing HPV: The same immune defects that raise cancer risk also make HPV infections more persistent, which is why ESRD cohorts show a 2–2.5‑fold higher incidence of HPV‑related cancers compared with the general population. Persistent high‑risk HPV infection is biologically linked to both genital warts (from certain types) and HPV‑related dysplasia and cancer.frontiersin+1
  • General HPV risk factors still matter: Systematic reviews of cutaneous warts (in mixed populations) note that smoking, close personal contact, communal environments, and atopy increase wart risk. For HPV‑associated cancers (which track high‑risk HPV exposure), smoking, alcohol, and HIV infection are important cofactors. These same factors likely identify the subgroup of ESRD patients more prone to clinically evident or persistent warts.onlinelibrary.wiley+2

Clinical wart pattern in ESRD

  • Low absolute prevalence, but higher than normal: Skin‑series in hemodialysis show warts in only a few percent of patients, yet this is still more frequent than in matched healthy controls, and authors explicitly list viral warts among the “most frequent viral infections” in CKD skin disease.healthcare-bulletin+2
  • Stubborn, chronic lesions: When warts appear in ESRD, clinicians describe them as more persistent and sometimes refractory, mirroring the broader experience of infections in ESRD patients.pmc.ncbi.nlm.nih+1
  • Association with other skin problems of CKD: Patients with xerosis, pruritus, pigment changes, and other CKD skin abnormalities are the same broad group in which warts are reported; warts are one item in this constellation rather than a distinct phenotype.ijdvl+2

Putting this together for “who gets warts” in ESRD

ESRD patients who develop warts typically have:

  • Long‑standing, advanced renal failure on dialysis with uremic immune dysfunction.actasdermo+1
  • Usual HPV exposure/risk factors (sexual exposure, close skin contact, sometimes smoking or other co‑morbid risks).pubmed.ncbi.nlm.nih+2
  • Age in mid‑ to later adulthood, where persistent HPV infection and HPV‑related disease are most evident.pmc.ncbi.nlm.nih

Unlike the transplant setting, there is no sharply defined “wart phenotype” (for example, specific drugs), but rather a background of modest immune fragility in ESRD that makes the usual HPV exposures more likely to result in chronic, slow‑to‑clear warts.

  1. https://pmc.ncbi.nlm.nih.gov/articles/PMC3710213/
  2. https://onlinelibrary.wiley.com/doi/10.1111/pde.16002
  3. https://pmc.ncbi.nlm.nih.gov/articles/PMC8061480/
  4. http://www.actasdermo.org/en-skin-manifestations-chronic-kidney-disease-articulo-S0001731015002720
  5. https://pmc.ncbi.nlm.nih.gov/articles/PMC4299702/
  6. https://karger.com/bpu/article/47/1-3/259/329355/Recognizing-Common-Skin-and-Soft-Tissue-Infections
  7. https://www.actasdermo.org/en-skin-manifestations-chronic-kidney-disease-articulo-S1578219015002346
  8. https://www.frontiersin.org/journals/pediatrics/articles/10.3389/fped.2022.1057454/full
  9. https://pubmed.ncbi.nlm.nih.gov/32503931/
  10. https://journals.sagepub.com/doi/abs/10.1136/jim-2019-001262
  11. https://www.healthcare-bulletin.co.uk/article/volume-14-issue-3-pages870-878-ra/
  12. https://ijdvl.com/cutaneous-manifestations-in-patients-with-chronic-renal-failure-on-hemodialysis/
  13. https://www.ijord.com/index.php/ijord/article/view/1234
  14. https://www.sciencedirect.com/science/article/pii/S1600613522089079
  15. https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2772021
  16. https://emedicine.medscape.com/article/1094846-overview
  17. https://www.semanticscholar.org/paper/Incidence-and-risk-factors-for-HPV-associated-in-Han-Waller/fe6a798835199fa86e050e34bcdb696514e80486
  18. https://onlinelibrary.wiley.com/doi/10.1111/ajt.14181
  19. https://nigjdermatology.com/index.php/NJD/article/download/31/6/121
  20. https://www.ectrx.org/detail/archive/2019/17/1/0/31/0
  21. https://academic.oup.com/ndt/article/32/1/132/2931147

Finance Friday: Buy or Not Buy Quantum Computing Stock?

I recently read in a WSJ article that companies in the nascent industry involving quantum computing are of great interest to investors. Several companies were listed as competing in the space, including QBTS. I then went to Perplexity and instructed it to accomplish Deep Research on this company. The embedded PDF below is the resultant report. Very well done and in great depth that directly and specifically addresses the questions posed in my prompt, as you may ascertain.

Prompt: Do deep research into the quantum stock QBTS: should I buy into it or not? If I buy, how many shares?

My Baby Loves Biscuits More Than Me

Please turn up your audio, watch the embedded video below, then read the following text about the video.

Otis Lee Booker is the fictional persona behind “My Baby Loves Biscuits More Than Me,” a song crafted to emulate an extremely rare 1939 Delta blues recording, but actually brought to life using AI-driven remastering and storytelling techniques in recent years. While some project pages and videos claim the track was rescued from old shellac discs and lost sessions in the Mississippi Delta, official disclaimers on these recent releases confirm that the backstory and character are creative inventions—the music is real, but the artist and his history are fabricated for the sake of tribute and parody.​

The song itself captures the humor, sorrow, and grit of Depression-era blues through a raw, playful tale of heartbreak and food, sung in a style that channels legendary Delta blues traditions. The internet reaction and write-ups treat Otis Lee Booker as a tongue-in-cheek homage to lost blues musicians whose lives and recordings have faded into legend, with cover versions and remix projects further amplifying the fictional lore.​

Separately, records exist for a real person named Otis Lee Booker Sr. (1962–1994) from Moss Point, Mississippi, but there is no evidence connecting this individual to blues music or the AI-driven song project described above.

Summary Table of Otis Lee Booker Trivia

AspectDescription
OriginsFictional bluesman created for tribute/parody projects, not a real historical figure. ​
Song“My Baby Loves Biscuits More Than Me” (AI-generated, styled after prewar Delta blues)​
Public ReactionPraised for humor and musical authenticity; acknowledged as an imaginative tribute​
Real IndividualsAn unrelated Otis Lee Booker Sr. (1962–1994) memorialized in Mississippi

Making Perplexity Work For You: Latest on Peritoneal Dialysis Research

I recently ordered a book from Amazon concerning Perplexity. In it, I discovered that the Pro version of Perplexity, which I am running, has something named Perplexity Pages. You can accomplish lots of tasks with this aspect of Perplexity, including constructing blogs, which I recently accomplished. See the embedded PDF below, which summarizes in specific detail, the latest research into Peritoneal Dialysis. I employed Perplexity’s built-in graphic tool to make the graphic. Notice that in the prompt I misspelled blog as log, and this web site’s URL which Perplexity corrected for the research.

Observation for those on Peritoneal Dialysis using Fresenius Cycler

I noticed the time I was spending on evening dialysis was creeping up, going from a 10-hour-plus range to over eleven hours. (Actual data: 10-52, 10-42, 10-24, 10-47, 10-58, 11-3, 11-0 indicating hours-minutes) (Mean 10-49 and Std Dev 12.44). This indicated something was not right. So I started a three-day regimen of using Heparin, one dose in my 2000 ml evening static fill (4 ml) and one dose in my 6 liter overnight fill (12 ml). After the first evening, I fell back to 10-39, a big jump in the right direction.

I suspect that I had/have a buildup of stuff slowing the process down, especially the drain cycle. Perplexity suggests “Heparin helps peritoneal dialysis patients primarily by reducing peritoneal inflammation and preventing fibrin formation, which can improve peritoneal fluid transport. Intraperitoneal heparin has anti-inflammatory and anticoagulant properties that reduce peritoneal permeability to small solutes and increase ultrafiltration volume, potentially leading to better fluid removal and reduced complications like fluid overload, hypertension, and peritoneal membrane damage. It also helps maintain catheter patency by preventing fibrin-induced blockages in the dialysis catheter.”

Whatever, two more self-inflicted treatments to go, and we should be good to go. BTW, had frost in places this morning here in North Texas, and it’s predicted to get down to 25F tonight. Getting to “burrr” weather.

The Mess I’m In: Dialysis Isn’t Always Pretty!

Well, my labs from last week are back. Took three days this time; usually one or two. Guess what? My Albumin did not budge. Although I continue to eat more protein and drink Costco protein drinks, it’s still at 3.4, way under the goal of 5.0. I have previously blogged that there is a lag between protein ingestion and results showing up in albumin, but this is recalcitrant behavior, like I can’t catch a break!

My phosphorus reading did come down to within acceptable limits, which is a bright spot!

I have previously alluded to having skin cancer essentially all over the exposed areas on my face, rear, neck, and head. The cancer has reached the stage in several areas where it is not healing, but staying open. Previously, I was having this treated via Moh’s Surgery, wherein chunks are cut out, looked at in the lab while I waited to ascertain if all the cancer was removed, and sent on my way. It takes about two weeks for this surgery to heal (for me), and as you might imagine, it is not the best way to enjoy life.

Last week, I saw an ad on TV for a company named Gentle Cure (website https://www.gentlecure.com/) that professed to be able to remove cancer. From their website: “Image-Guided SRT (Image-Guided Superficial Radiation Therapy) is a type of radiation used just for skin cancer. It kills skin cancer cells using low levels of X-ray energy. This energy is like what dentists use to X-ray teeth. It is given by a Radiation Therapist in a dermatologist’s office.

Image-Guided SRT is the first and only radiation treatment for skin cancer that uses ultrasound images. The ultrasound images let your dermatologist see the exact size of the cancer so he or she can target the area with the precise dose. These images also show the cancer shrinking and going away after each treatment.” I have embedded their PR video at the end.

I have an appointment tomorrow at 10 to get checked out. Wish me luck!

Lastly, two nights ago, the swab I used to clean my catheter port turned up pinkish. Last night, I had a blood spot about the size of a quarter on my bandage used to cover the area. I’m going back to three nights of Heprin treatment, and my wife is going to check me out this evening. Just something else to deal with.

Welcome to the world of Peritoneal Dialysis. No one said it was going to be easy!

Financial Friday: Using Perplexity to Calculate Dividends

One of the questions that may be posed when musing over your stock portfolio is about stock dividends. Often, the information provided by brokerages is misleading or incomplete. For example, our brokerage, Schwab, only aggregates dividends and provides simplistic results, such as the dividend return is the total amount of dividends divided by the cost of stocks. This neglects the compounding effect of using a stock’s DRIP (Dividend Reinvestment Program).

To address this situation, I am going to use actual numbers from a stock in our portfolio, Trinity Capital, with ticker symbol TRIN. In this example, I want to know what is provided in the following Prompt and provide results in a table format that follows. Note that instead of a static $1970.13 in quarterly dividends, the last quarter in 2026 TRIN paid out $2252.04 in dividends with a total payout of $10,488.41.

Prompt: Current date 10/31/2025. We own 3863 shares of BDC TRIN, which are in their DRIP. Calculate quarterly dividends and construct a table with values of dividend, # shares DRIP, total number of shares held, and total dividends paid to date, all through the last payment in December 2026.

Here is the table limited to only the months in which TRIN pays its regular dividends—December, March, June, and September. It includes dividend paid, the number of new shares added via DRIP, total shares after reinvestment, and cumulative total dividends paid through the last payment in December 2026.

TRIN DRIP Table (Dividend Months Only: Dec, Mar, Jun, Sep)

MonthDividendShares DRIPTotal SharesCumulative Div Paid
2025-121970.13131.34203994.34201970.13
2026-032037.11135.80774130.14974007.24
2026-062083.90138.92694269.07666091.14
2026-092145.23143.01524412.09188236.37
2026-122252.04150.13634562.228110488.41
  • Only dividend-paying months are listed, matching TRIN’s expected payout pattern.
  • “Shares DRIP” is the rounded estimate of new shares bought using the dividend (assumes a $15 share price).
  • Dividends and share totals are cumulative and project only regular quarterly payouts. Supplemental or variable dividends are not included.

These updated values illustrate your DRIP growth and total dividends by each quarter through the end of 2026.

Bear With Me: Monte Carlo and Me and Perplexity

Monte Carlo methods originated in the mid-20th century, although early concepts date to the 18th century. The pivotal modern development happened during World War II with Stanislaw Ulam, who, while working at Los Alamos National Laboratory on nuclear weapons research, conceived random sampling as a way to solve complex neutron diffusion problems that defied standard mathematical analysis.wikipedia+6

Early Mathematical Roots

  • The initial concept can be traced to experiments like Buffon’s needle in the 18th century, where French scientist Georges Louis LeClerc (Comte de Buffon) used repeated random trials to estimate mathematical values, notably Pi.pmc.ncbi.nlm.nih+1
  • In the 19th century, simulation and randomization methods continued to develop in statistics and probability studies, such as smoothing mortality tables and generating distributions with dice and cards.pmc.ncbi.nlm.nih

World War II and the Manhattan Project

  • The method’s breakthrough came in the 1940s at Los Alamos. Stanislaw Ulam, recovering from illness and playing solitaire, realized some problems—like predicting the likelihood of winning the game or neutron movement in reactors—could be addressed by simulating many random outcomes and observing their frequencies.oakleyj.github
  • Ulam shared his idea with John von Neumann, who recognized its power and helped formalize the computational implementation. The approach was first coded for the ENIAC electronic computer in 1948.lanl+1
  • The term “Monte Carlo” was coined by Nicholas Metropolis, inspired by both the randomness of the method and the famed Monte Carlo Casino, symbolizing luck and probabilistic games.investopedia+1

Key Contributors

  • Stanislaw Ulam: Conceived and refined the central concept.oakleyj.github
  • John von Neumann: Helped formalize and implement the numerical technique.aws.amazon+1
  • Nicholas Metropolis: Named the method and contributed to coding and applications.metaplane+1

Monte Carlo methods revolutionized simulation and modeling, becoming foundational in physics, finance, engineering, and data science.investopedia+2

What Are Monte Carlo Simulations?

Monte Carlo simulations are mathematical techniques that use random sampling from defined probability distributions to create a wide range of possible scenarios for a given problem. Instead of relying on single-point predictions, the process repeats thousands—even millions—of iterations, each drawing random values for input variables. This results in a comprehensive picture of potential outcomes and their likelihoods.investopedia+3

How Do They Work?

The basic workflow involves:

  • Defining uncertain variables (such as market returns, costs, project delays).mastt+2
  • Assigning each variable a probability distribution that reflects its possible range (e.g., normal, triangular, uniform).mastt
  • Running thousands of iterations, each randomly sampling values from these distributions.lumivero+1
  • Aggregating all results to produce a probability distribution of outcomes.lumivero+1

For example, in finance, if one wants to forecast retirement portfolio sustainability, a Monte Carlo Simulation would vary market returns, inflation rates, interest rates, and more, then review the range and probability of possible outcomes.emoneyadvisor+2

Real-World Applications

In finance, Monte Carlo methods help analyze:

  • Portfolio return variability and risk
  • Retirement income sustainability projectionsanalytica+1
  • Stock option pricing by simulating asset price paths and payoffsinvestopedia+1
  • Asset-liability modeling in pensions and insurance
  • Risk assessment, including “Value at Risk” and stress testinginteractivebrokers+1

Beyond finance, these methods are widely used for:

  • Project cost, schedule, and risk modeling in engineeringlumivero+1
  • Reliability and efficiency forecasts in manufacturinglumivero
  • Estimating solutions to complex mathematical problems, such as approximating Pi or infinite seriesmetaplane

A Simple Example: Predicting Stock Price

First, I’m going to outline the problem we are going to use Monte Carlo techniques to address, then write a Perplexity Prompt to actually use Monte Carlo to solve, and lastly, the results provided by Monte Carlo. At this point, you may be asking yourself Why? It falls in the “because I can class” and also to point out some of the less evident things Perplexity can do for you, if you are so inclined.

I have been tracking and buying a significant position in a stock with the ticker TRIN. It is a BDC company with a current 13.1% simple annualized return, pays dividends quarterly, at $0.51 per share. Recently, the stock dropped 4.5% in a single day, which I viewed as a buying opportunity. I had been buying TRIN at over $15.00, and accordingly, it was now in the $14.40 vicinity. I bought 1000 shares at 14.005.

Let’s assume TRIN’s price fits a triangle distribution. The triangular distribution is a continuous probability distribution shaped like a triangle, defined by three parameters: the minimum value aa, the maximum value bb, and the mode (or most likely value) cc, where a<ba<b and a≤c≤ba≤c≤b. It’s widely used when limited data is available, as it allows for the estimation of these three values, making it popular in project management, risk analysis, and Monte Carlo simulation work.wikipedia+4

You can generally get C-level executives to estimate next year’s sales as worst case, best case, and most likely after pounding heads for a while. Same thing for other estimates, which is the power of the triangle distribution. For TRIN, let’s assume the lowest price to expect is $14.00, the highest 18, and the most likely 16. We have everything we need to run a Monte Carlo simulation except the number of iterations. Let’s arbitrarily set this at 100.

Prompt: Run a Monte Carlo using the following: a triangular distribution with lowest value 14, highest 18, and most likely 16, using 100 iterations. Place the results in a table along with the probabilities of each histogram bin you provide.

Here is the extended table including the probability values for each bin in the Monte Carlo simulation from a triangular distribution with minimum 14, mode 16, and maximum 18, based on the PDF integration over each bin’s interval:

Bin RangeCountPDF Value (Height)Probability (Area of bin)
14.0–14.8100.1250.100
14.8–15.6180.31250.225
15.6–16.4380.50.320
16.4–17.2220.31250.225
17.2–18.0120.1250.130

Explanation:

  • Count: Number of samples in the bin from the simulation.
  • PDF Value: The height of the triangular probability density function at the midpoint of the bin.
  • Probability: The integral (area) of the PDF over the bin range, representing the probability that a random variable falls within that interval.

These probability values sum approximately to 1 (due to rounding), confirming that the bins collectively cover the entire probability space for this distribution. This table reflects how the triangular distribution assigns higher probabilities near the mode and lower toward the minimum and maximum values, aligning with the Monte Carlo simulation output.statology+2

And that, kind folks, is how you make Perplexity do weird statistical stuff for you!

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