BeFreed
    Categories>Finance & Economics>Return Mathematics: Liquid vs Illiquid Investing

    Return Mathematics: Liquid vs Illiquid Investing

    20 min
    |
    |
    Nov 25, 2025
    FinanceBusinessScience

    Deep dive into the sophisticated mathematical frameworks transforming portfolio theory, from GARCH models to liquidity premiums, revealing how quantitative methods optimize returns across liquid and illiquid investment strategies.

    Return Mathematics: Liquid vs Illiquid Investing

    Best quote from Return Mathematics: Liquid vs Illiquid Investing

    “

    Traditional portfolio theory treats all assets as if they're perfectly liquid, but that's mathematically naive. When you're dealing with illiquid alternatives, you need stochastic linear system models to properly capture random capital calls, uncertain distributions, and time delays.

    ”

    This audio lesson was created by a BeFreed community member

    Input question

    return and rate mathematics in the quantitative foundations of investing in liquid and illiquid strategies

    Host voices
    Niaplay
    Eliplay
    Knowledge sources
    Asset Allocation
    Strategic Risk Management
    Strategic Asset Allocation with Illiquid Alternatives - arXiv
    link
    https://arxiv.org/pdf/2207.07767
    Systematic Trading
    Liquidity Premium, Liquidity-Adjusted Return and Volatility, and a Unified Modern Portfolio Theory: illustrated with Crypto Assets
    link
    https://export.arxiv.org/pdf/2306.15807v3.pdf
    The Wrapper Matters: Comparing Liquid Alternatives and Hedge Funds
    link
    https://caia.org/sites/default/files/thewrapper.pdf

    Discover more

    Learn to invest in public & private markets

    Learn to invest in public & private markets

    LEARNING PLAN

    Learn to invest in public & private markets

    This comprehensive curriculum bridges the gap between traditional stock analysis and exclusive private market strategies used by institutional investors. It is designed for ambitious individuals looking to move beyond basic saving toward sophisticated wealth management and advanced asset allocation.

    3 h 1 m•4 Sections
    Invest, Economics, Politics & Finance

    Invest, Economics, Politics & Finance

    LEARNING PLAN

    Invest, Economics, Politics & Finance

    This comprehensive track bridges the gap between macroeconomic theory and practical investment execution. It is ideal for aspiring investors and professionals seeking to understand how geopolitical shifts and economic principles directly influence portfolio performance.

    2 h 29 m•4 Sections
    Investing & history

    Investing & history

    LEARNING PLAN

    Investing & history

    This learning plan bridges timeless investment wisdom with practical portfolio construction skills, essential for anyone seeking to build lasting wealth through markets. It's ideal for aspiring investors, finance professionals, or anyone managing their own retirement accounts who wants to move beyond surface-level knowledge and understand both the principles and historical context that separate successful long-term investors from speculators.

    1 h 49 m•4 Sections
    Learn to invest.

    Learn to invest.

    LEARNING PLAN

    Learn to invest.

    This comprehensive plan bridges the gap between basic financial literacy and advanced wealth-building strategies. It is ideal for aspiring investors who want to combine technical portfolio construction with the psychological discipline required for market success.

    3 h 46 m•4 Sections
    To be better in ecomics

    To be better in ecomics

    LEARNING PLAN

    To be better in ecomics

    This plan bridges the gap between theoretical models and real-world financial realities. It is ideal for professionals or students seeking to understand the psychological and systemic forces that drive global markets.

    3 h 11 m•4 Sections
    MATHS

    MATHS

    LEARNING PLAN

    MATHS

    This learning plan provides a comprehensive bridge between foundational arithmetic and advanced theoretical concepts. It is ideal for students or professionals looking to sharpen their analytical skills and understand the mathematical logic behind real-world data.

    3 h 18 m•4 Sections
    Become better at math and logic.

    Become better at math and logic.

    LEARNING PLAN

    Become better at math and logic.

    This plan is designed for individuals looking to sharpen their analytical skills and move beyond rote memorization to true mathematical fluency. It is ideal for professionals, students, or lifelong learners who want to improve their decision-making and logical rigor.

    2 h 45 m•4 Sections
    Study Finance, Behavior & Memoirs

    Study Finance, Behavior & Memoirs

    LEARNING PLAN

    Study Finance, Behavior & Memoirs

    This plan bridges the gap between technical financial literacy and the psychological factors that drive market success. It is ideal for aspiring investors who want to master both the mechanics of wealth building and the behavioral discipline required to sustain it.

    2 h 44 m•4 Sections

    From Columbia University alumni built in San Francisco

    BeFreed Brings Together A Global Community Of 1,000,000 Curious Minds
    See more on how BeFreed is discussed across the web

    "Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

    @Moemenn
    platform
    star
    star
    star
    star
    star

    "I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

    @Chloe, Solo founder, LA
    platform
    comments
    12
    likes
    117

    "Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

    @Raaaaaachelw
    platform
    star
    star
    star
    star
    star

    "Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

    @Matt, YC alum
    platform
    comments
    12
    likes
    108

    "Reading used to feel like a chore. Now it’s just part of my lifestyle."

    @Erin, Investment Banking Associate , NYC
    platform
    comments
    254
    likes
    17

    "Feels effortless compared to reading. I’ve finished 6 books this month already."

    @djmikemoore
    platform
    star
    star
    star
    star
    star

    "BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

    @Pitiful
    platform
    comments
    96
    likes
    4.5K

    "BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

    @SofiaP
    platform
    star
    star
    star
    star
    star

    "BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

    @Jaded_Falcon
    platform
    comments
    201
    thumbsUp
    16

    "It is great for me to learn something from the book without reading it."

    @OojasSalunke
    platform
    star
    star
    star
    star
    star

    "The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

    @Leo, Law Student, UPenn
    platform
    comments
    37
    likes
    483

    "Makes me feel smarter every time before going to work"

    @Cashflowbubu
    platform
    star
    star
    star
    star
    star

    From Columbia University alumni built in San Francisco

    BeFreed Brings Together A Global Community Of 1,000,000 Curious Minds
    See more on how BeFreed is discussed across the web

    "Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

    @Moemenn
    platform
    star
    star
    star
    star
    star

    "I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

    @Chloe, Solo founder, LA
    platform
    comments
    12
    likes
    117

    "Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

    @Raaaaaachelw
    platform
    star
    star
    star
    star
    star

    "Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

    @Matt, YC alum
    platform
    comments
    12
    likes
    108

    "Reading used to feel like a chore. Now it’s just part of my lifestyle."

    @Erin, Investment Banking Associate , NYC
    platform
    comments
    254
    likes
    17

    "Feels effortless compared to reading. I’ve finished 6 books this month already."

    @djmikemoore
    platform
    star
    star
    star
    star
    star

    "BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

    @Pitiful
    platform
    comments
    96
    likes
    4.5K

    "BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

    @SofiaP
    platform
    star
    star
    star
    star
    star

    "BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

    @Jaded_Falcon
    platform
    comments
    201
    thumbsUp
    16

    "It is great for me to learn something from the book without reading it."

    @OojasSalunke
    platform
    star
    star
    star
    star
    star

    "The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

    @Leo, Law Student, UPenn
    platform
    comments
    37
    likes
    483

    "Makes me feel smarter every time before going to work"

    @Cashflowbubu
    platform
    star
    star
    star
    star
    star

    "Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

    @Moemenn
    platform
    star
    star
    star
    star
    star

    "I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

    @Chloe, Solo founder, LA
    platform
    comments
    12
    likes
    117

    "Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

    @Raaaaaachelw
    platform
    star
    star
    star
    star
    star

    "Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

    @Matt, YC alum
    platform
    comments
    12
    likes
    108

    "Reading used to feel like a chore. Now it’s just part of my lifestyle."

    @Erin, Investment Banking Associate , NYC
    platform
    comments
    254
    likes
    17

    "Feels effortless compared to reading. I’ve finished 6 books this month already."

    @djmikemoore
    platform
    star
    star
    star
    star
    star

    "BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

    @Pitiful
    platform
    comments
    96
    likes
    4.5K

    "BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

    @SofiaP
    platform
    star
    star
    star
    star
    star

    "BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

    @Jaded_Falcon
    platform
    comments
    201
    thumbsUp
    16

    "It is great for me to learn something from the book without reading it."

    @OojasSalunke
    platform
    star
    star
    star
    star
    star

    "The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

    @Leo, Law Student, UPenn
    platform
    comments
    37
    likes
    483

    "Makes me feel smarter every time before going to work"

    @Cashflowbubu
    platform
    star
    star
    star
    star
    star

    "Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

    @Moemenn
    platform
    star
    star
    star
    star
    star

    "I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

    @Chloe, Solo founder, LA
    platform
    comments
    12
    likes
    117

    "Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

    @Raaaaaachelw
    platform
    star
    star
    star
    star
    star

    "Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

    @Matt, YC alum
    platform
    comments
    12
    likes
    108

    "Reading used to feel like a chore. Now it’s just part of my lifestyle."

    @Erin, Investment Banking Associate , NYC
    platform
    comments
    254
    likes
    17

    "Feels effortless compared to reading. I’ve finished 6 books this month already."

    @djmikemoore
    platform
    star
    star
    star
    star
    star

    "BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

    @Pitiful
    platform
    comments
    96
    likes
    4.5K

    "BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

    @SofiaP
    platform
    star
    star
    star
    star
    star

    "BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

    @Jaded_Falcon
    platform
    comments
    201
    thumbsUp
    16

    "It is great for me to learn something from the book without reading it."

    @OojasSalunke
    platform
    star
    star
    star
    star
    star

    "The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

    @Leo, Law Student, UPenn
    platform
    comments
    37
    likes
    483

    "Makes me feel smarter every time before going to work"

    @Cashflowbubu
    platform
    star
    star
    star
    star
    star
    1.5K Ratings4.7
    Start your learning journey, now
    BeFreed App
    BeFreed

    Learn Anything, Personalized

    DiscordLinkedIn
    Featured book summaries
    Crucial ConversationsThe Perfect MarriageInto the WildNever Split the DifferenceAttachedGood to GreatSay Nothing
    Trending categories
    Self HelpCommunication SkillRelationshipMindfulnessPhilosophyInspirationProductivity
    Celebrities' reading list
    Elon MuskCharlie KirkBill GatesSteve JobsAndrew HubermanJoe RoganJordan Peterson
    Award winning collection
    Pulitzer PrizeNational Book AwardGoodreads Choice AwardsNobel Prize in LiteratureNew York TimesCaldecott MedalNebula Award
    Featured Topics
    ManagementAmerican HistoryWarTradingStoicismAnxietySex
    Best books by Year
    2025 Best Non Fiction Books2024 Best Non Fiction Books2023 Best Non Fiction Books
    Featured authors
    Chimamanda Ngozi AdichieGeorge OrwellO. J. SimpsonBarbara O'NeillWinston ChurchillCharlie Kirk
    BeFreed vs other apps
    BeFreed vs. Other Book Summary AppsBeFreed vs. ElevenReaderBeFreed vs. ReadwiseBeFreed vs. Anki
    Learning tools
    Knowledge VisualizerAI Podcast Generator
    Information
    About Usarrow
    Pricingarrow
    FAQarrow
    Blogarrow
    Careerarrow
    Partnershipsarrow
    Ambassador Programarrow
    Directoryarrow
    BeFreed
    Try now
    © 2026 BeFreed
    Term of UsePrivacy Policy
    BeFreed

    Learn Anything, Personalized

    DiscordLinkedIn
    Featured book summaries
    Crucial ConversationsThe Perfect MarriageInto the WildNever Split the DifferenceAttachedGood to GreatSay Nothing
    Trending categories
    Self HelpCommunication SkillRelationshipMindfulnessPhilosophyInspirationProductivity
    Celebrities' reading list
    Elon MuskCharlie KirkBill GatesSteve JobsAndrew HubermanJoe RoganJordan Peterson
    Award winning collection
    Pulitzer PrizeNational Book AwardGoodreads Choice AwardsNobel Prize in LiteratureNew York TimesCaldecott MedalNebula Award
    Featured Topics
    ManagementAmerican HistoryWarTradingStoicismAnxietySex
    Best books by Year
    2025 Best Non Fiction Books2024 Best Non Fiction Books2023 Best Non Fiction Books
    Learning tools
    Knowledge VisualizerAI Podcast Generator
    Featured authors
    Chimamanda Ngozi AdichieGeorge OrwellO. J. SimpsonBarbara O'NeillWinston ChurchillCharlie Kirk
    BeFreed vs other apps
    BeFreed vs. Other Book Summary AppsBeFreed vs. ElevenReaderBeFreed vs. ReadwiseBeFreed vs. Anki
    Information
    About Usarrow
    Pricingarrow
    FAQarrow
    Blogarrow
    Careerarrow
    Partnershipsarrow
    Ambassador Programarrow
    Directoryarrow
    BeFreed
    Try now
    © 2026 BeFreed
    Term of UsePrivacy Policy

    Part of a Learning Plan

    Hedge Portfolio Risk with Derivatives

    Hedge Portfolio Risk with Derivatives

    LEARNING PLAN

    Hedge Portfolio Risk with Derivatives

    2 h 59 m•4 Episodes

    Key Takeaways

    1

    Opening and Setting the Stage

    0:00
    0:21
    0:40
    2

    Foundational Mathematics of Asset Allocation

    1:03
    1:25
    1:43
    2:03
    2:28
    2:49
    3

    The Illiquidity Premium and Mathematical Modeling

    3:11
    3:29
    3:49
    4:14
    4:35
    4:54
    4

    Systematic Trading and Risk Management Mathematics

    5:16
    5:34
    5:52
    6:14
    6:30
    6:48
    5

    Liquidity-Adjusted Portfolio Theory Mathematics

    7:09
    7:23
    7:44
    8:02
    8:20
    8:39
    8:58
    6

    Strategic Risk Management and Dynamic Hedging

    9:18
    9:34
    9:54
    10:12
    10:30
    10:51
    7

    Liquid Alternatives versus Hedge Fund Mathematics

    11:07
    11:24
    11:38
    11:58
    12:16
    12:33
    8

    Correlation Dynamics and Portfolio Mathematics

    12:52
    13:09
    13:23
    13:47
    14:05
    14:31
    9

    Advanced Mathematical Modeling Techniques

    14:46
    15:04
    15:24
    15:38
    15:54
    16:08
    10

    Practical Implementation and Mathematical Constraints

    16:23
    16:39
    17:03
    17:25
    17:41
    17:57
    11

    Wrapping Up: The Mathematical Revolution in Portfolio Theory

    18:19
    1:43
    18:59
    19:19
    19:35
    19:55
    20:10
    20:26

    More like this

    The Math Behind Smart Money book cover
    The Four Pillars of InvestingThe Logic Of Sports BettingA Random Walk Down Wall StreetThe Misbehavior of Markets
    24 sources
    The Math Behind Smart Money
    Discover the essential mathematical concepts that separate successful investors from the crowd. From basic statistics to advanced portfolio theory, learn the quantitative tools you need to make smarter investment decisions.
    27 min
    Technical Financial Fundamentals Deep Dive book cover
    source 1source 2The Ultimate Guide to the Three Financial Statementssource 4
    6 sources
    Technical Financial Fundamentals Deep Dive
    Master advanced financial analysis through mathematical precision - from balance sheet equations and cash flow modeling to risk measurement, portfolio optimization, and valuation techniques that professional investors use.
    23 min
    Capital Returns book cover
    Capital Returns
    Edward Chancellor
    Insightful guide to the capital cycle approach, offering strategic investment wisdom for navigating market dynamics and maximizing returns.
    9 min
    Modern investment strategies and why old playbooks fail book cover
    Stock Investing for DummiesThe Intelligent Asset AllocatorFalcon MethodThe Intelligent Investor
    30 sources
    Modern investment strategies and why old playbooks fail
    Traditional portfolios are struggling as market correlations break down. Learn how top institutions adapt their analysis to find consistency in 2026.
    28 min
    Mastering the $132 Trillion Asset Management Game book cover
    The Intelligent Asset AllocatorAsset AllocationThe Little Book That Makes You RichA Wealth of Common Sense
    20 sources
    Mastering the $132 Trillion Asset Management Game
    Discover how effective asset management works beyond buying low and selling high - from personal portfolios to business equipment, learn the systematic approach to maximizing value while minimizing risk.
    35 min
    Beyond Stocks and Bonds: Asset Classes Explained book cover
    What Are Asset Classes? More Than Just Stocks and BondsA masterclass on the major asset classesAsset classes explained: Cash, bonds, real estate and equitiessource 4
    6 sources
    Beyond Stocks and Bonds: Asset Classes Explained
    Discover the hidden universe of investment opportunities beyond traditional stocks and bonds. Learn how real estate, commodities, and alternative strategies can transform your portfolio's risk and returns.
    10 min
    The Visual Investor book cover
    The Visual Investor
    John J. Murphy
    Master technical analysis and spot market trends using visual charts, empowering individual investors to make smarter trading decisions.
    9 min
    The Great Mental Models Volume 3 book cover
    The Great Mental Models Volume 3
    Rhiannon Beaubien and Rosie Leizrowice
    Master systems and math to navigate life intelligently
    10 min