The geometry of risk adjustments
(2023) In Decisions in Economics and Finance- Abstract
We present a geometric approach to portfolio theory with a focus on risk-adjusted returns, in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations, especially in higher dimensions, only minor conceptual modifications (e.g., using orthogonal Sharpe ratios rather than risk-adjusted returns) are needed to identify the efficient trading strategies. We further show that, in a complete market, the so-called market price of risk vector is identical to the growth optimal Kelly vector, albeit expressed in coordinates of a different basis. This implies that a derivative, having an orthogonal Sharpe ratio of zero, has a price given by the minimal martingale measure.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1993a83a-95ae-4b00-92de-abe31f05c304
- author
- Bermin, Hans Peter LU and Holm, Magnus
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- epub
- subject
- keywords
- Geometry, Jensen’s alpha, Kelly criterion, Market price of risk, Option pricing
- in
- Decisions in Economics and Finance
- publisher
- Springer
- external identifiers
-
- scopus:85179691408
- ISSN
- 1593-8883
- DOI
- 10.1007/s10203-023-00421-1
- language
- English
- LU publication?
- yes
- id
- 1993a83a-95ae-4b00-92de-abe31f05c304
- date added to LUP
- 2024-01-10 15:48:02
- date last changed
- 2024-01-25 14:13:02
@article{1993a83a-95ae-4b00-92de-abe31f05c304,
abstract = {{<p>We present a geometric approach to portfolio theory with a focus on risk-adjusted returns, in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations, especially in higher dimensions, only minor conceptual modifications (e.g., using orthogonal Sharpe ratios rather than risk-adjusted returns) are needed to identify the efficient trading strategies. We further show that, in a complete market, the so-called market price of risk vector is identical to the growth optimal Kelly vector, albeit expressed in coordinates of a different basis. This implies that a derivative, having an orthogonal Sharpe ratio of zero, has a price given by the minimal martingale measure.</p>}},
author = {{Bermin, Hans Peter and Holm, Magnus}},
issn = {{1593-8883}},
keywords = {{Geometry; Jensen’s alpha; Kelly criterion; Market price of risk; Option pricing}},
language = {{eng}},
publisher = {{Springer}},
series = {{Decisions in Economics and Finance}},
title = {{The geometry of risk adjustments}},
url = {{http://dx.doi.org/10.1007/s10203-023-00421-1}},
doi = {{10.1007/s10203-023-00421-1}},
year = {{2023}},
}