Happy New Year and Some News

1 January 2024

Happy New Year to everyone!

We trust you all had a nice Christmas break and raring to go in 2024.

A couple of bits of news from us.

First, our article “Arbitrage Problems with Reflected Geometric Brownian Motion” has just been published. The full reference and the Open Access link is given here:

Arbitrage Problems with Reflected Geometric Brownian Motion.” (D.E. Buckner, K. Dowd and H. Hulley) Finance and Stochastics (2023) 28: 1-26.

We will have more to say on reflected GBM processes soon, as Annals of Actuarial Statistics, the journal that published Guy Thomas’s devastatingly flawed articles on the subject, seems to think it is OK to published flawed models that could bankrupt a company that uses them, without allowing anyone (i.e. us) to make any comment to that effect in its hallowed pages. This is like a maths journal that publishes an article saying that 2 plus 2 equals 5, and that’s OK because 2 plus 2 equals 4 is merely an opinion and other actuaries might have a different opinion.

We will how well that opinion holds up in due course. We have a cunning plan to address this issue.

Second, my new book on free banking is out. The link is:

The Experience of Free Banking, second edition.

There is a blog on it here, which also explains what free banking actually is.

Arbitrage Problems with Reflected Geometric Brownian Motion

Good news!

 

Our article, “Arbitrage Problems with Reflected Geometric Brownian Motion” by Dean Buckner, Kevin Dowd and Hardy Hulley, has just been accepted for publication by the prestigious journal Finance and Stochastics.

The abstract of the article states:

 

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numeraire portfolios or equivalent risk-neutral probability measures, which makes them totally unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

 

What this means in plain English is that our friend Guy Thomas’s article “Valuation of no-negative-equity guarantees with a lower reflecting barrier” in the Annals of Actuarial Science in 2020 is wrong, dead wrong.

Continue reading “Arbitrage Problems with Reflected Geometric Brownian Motion”

New ERM publication

We are pleased to announce that our long-waited ‘definitive’ article on ERM valuation has just been published in the Journal of Demographic Economics. The full citation is:

Buckner, K. Dowd and H. Hulley (2023) “A Market Consistent Approach to the Valuation of No-Negative Equity Guarantees and Equity Release Mortgages.” Journal of Demographic Economics Vol 89, pp. 349–372. https://doi.org/10.1017/dem.2023.6.

We welcome Dr. Hardy Hulley from UTS Sydney to our ERM working party.

Another brick in the wall tank on the lawn for the Institute and Faculty of Actuaries.

Anyone who has any trouble downloading the article please just drop us a line and we will send it to you.

The Harry I Knew

Roger J. Brown

[This guest posting from Dr. Roger Brown from his latest MathEstate newsletter gives a uniquely personal obituary to the late, great Harry Markowitz, the inventor of modern portfolio theory. Harry died in San Diego on 22 June 2023 at the age of 95. May he rest in peace.]

Lost one of my heroes

In the final year of the last Century, my last year of Graduate School, the San Diego Union Tribune did an article on Harry Markowitz. Thus, I learned he and I lived in the same city. Of course, I called him up to propose a lunch. Lucky for me he said “Yes.” It was before cellphone cameras. To that first lunch I brought a small “point-and-shoot” camera which I asked his assistant to use.

Unfortunately, I did not notice it was set on “Panoramic” which provided a very wide view of many things except, ironically, the heads of the subjects. Harry was 6’4”. For years a picture hung in my office of two hands shaking in front of Harry Markowitz’s belt buckle. Thus began a great friendship.

He towered over me in all respects. He embodied the best of what it meant to be an academic. To those who value rational thinking he was a National Treasure. Every bit equal to his academic accomplishments was his humanity. At that first lunch he described his penchant for putting 25-year-old balsamic vinegar on ice cream. He liked to cook. We exchanged recipes for more than two decades.

His sense of humor was grand. We had heard many of the same jokes but delighted in telling variants of them over again to each other. When, rarely, I had one he had not heard he relished it, doubling over in laughter. It occurred to me that if my greatest accomplishment in academia was making Harry laugh, that would be enough.

Rational in all areas, his health was no exception. For years I would set aside an entire afternoon for our regular lunch, knowing it would be preceded and followed by a long walk. During those walks we discussed all manner of things, academics, mathematics, art and theater, family and, of course, economics.

He shared my bemused interest in politics, wondering right alongside me and everyone else where those whacky ideas came from and who really believed they would work.

His own pure rationality was tempered and tested by his devotion to his wife, Barbara. I was glad to have had the chance to tell him what I admired most in him was his care for her. When the COVID pandrossy ruined plans for their 50th wedding anniversary, I know it was a big disappointment.

He was always writing. He thought he had something to say, and he was right. His view of the world influenced finance; his view of life influenced me. I was so lucky. I heard some of the best things Harry had to say directly from him.

Naturally, we both slowed over the years. I once told him I had made it to the age he was when we first met. He was not impressed. After he turned 90, he was fond of saying that it was too late for him to “die tragically.” The walks got shorter but if the spring in his step lagged, his mind never did. He was always in search of a puzzle, a pun or a way to see life like no one else.

We all should emulate my friend whom I often referred to, in his presence and with a hint of foolishness, as “The Great Man.” The truth is Harry enjoyed being Harry. We are all the richer for it.

Harry’s incredible mind gave us Modern Portfolio Theory. More importantly, his wonderful heart gave rationality a good name.

 

Still winning

We commented here in May 2022 on some specular forecasting failures, even by the Bank’s standards.

August 2020 “In the MPC’s central [inflation] projection, conditioned on prevailing market yields, CPI inflation is expected to be around 2% in two years’ time. [i.e. August 2022]”

August 2021 “… The MPC expects CPI inflation to rise temporarily to around 4% in the near term, before falling back towards 2%. … Inflation starts to decline in 2022, and returns to the 2% target in late 2023”

Hat tip to ‘The Courgette’ who has helpfully continued this sad story in an FT comment here.

Continue reading “Still winning”

UK sets out plans for failing insurers

The HM Treasury Consultation document is here,  setting out the government’s proposal to introduce a dedicated insurer resolution regime in the UK.

It would be so tempting to reply asking why such a regime would be necessary, given that insurer capital is determined by Solvency II to a 1 in 200 year event of insolvency, and that all insurers have a capital buffer well in excess of the required amount, making insolvency something like a 1 in 10,000 year event. The government doesn’t plan for asteroids hitting Westminster, why plan for insurers going bust? Could never happen.

(Irony)

Potential equity release mis-selling?

We were also quoted in the Telegraph yesterday on potential equity release misselling.

Kevin Dowd, professor of finance and economics at Durham University, said misselling is “always a risk” with commission-driven sales and the equity release sector “has a less than stellar record in this area”.

Dean Buckner, policy director of UK Shareholders Association, formerly of the Bank of England, said ideally struggling homeowners would downsize to a smaller property and invest for a better income, adding: “Instead, they are being encouraged to take out equity release at currently high rates.”

Mr Buckner said homeowners were at risk of being sold loans that were not appropriate to them. He said: “There is a temptation for financial advisers not to dwell on these aspects, and providers should think carefully about how this could be viewed as mis-selling by future regulators.”