Introduction to Digital Assets: formula sheet

Key formulas

Block linkage

Block n contains: transactions + timestamp + hash of block (n − 1)

Changing an old block changes its hash and breaks every later block. This gives tamper resistance.

Key roles

Private key signs ➜ public key verifies

The private key proves ownership. Never share it. The public key (or address derived from it) can be shared.

Proof of work

Security from computing cost: miners spend energy and hardware

Attacking requires controlling most of the computing power (a 51% attack).

Proof of stake

Security from economic stake: validators lock coins and risk losing them

Attacking requires controlling a large share of the staked coins. Lower energy use than PoW.

DLT versus traditional ledger

Traditional: one central record keeper. DLT: many nodes, each with a copy, synchronized by consensus

DLT removes the need for a single trusted intermediary, but it does not remove all risks.

Cryptocurrency

Decentralized issuance, no central issuer, no claim on an asset

Value comes from market supply and demand. Example: Bitcoin.

Stablecoin

Value pegged to a reference asset (often a fiat currency)

Check the backing: reserves, collateral or algorithm. Peg can break.

Security token

Token = digital claim on ownership or cash flows

Generally treated as a security and regulated as one.

Utility token

Token = access to a platform's product or service

No ownership or profit claim by design.

NFT

Unique, non-fungible token tied to a specific item

Not interchangeable one-for-one with another NFT.

CBDC

Digital fiat currency issued by a central bank

A central bank liability; centrally controlled.

Permissionless network

Open access + anonymous or pseudonymous participants + public data + decentralized governance

Typical features, not absolute rules. Examples: Bitcoin, Ethereum.

Permissioned network

Authorized access + known participants + restricted data + central or consortium governance

Typical features. Used where privacy, control and compliance matter.

Trade-off rule

More openness → more decentralization and transparency, less privacy and control

Reverse for permissioned networks.

Hot vs cold wallet

Hot = online, convenient, higher hacking risk | Cold = offline, safer from hacking, less convenient

Both store keys, not coins. Losing the private key means losing access.

Centralized vs decentralized exchange

Centralized = operator matches orders and often holds assets | Decentralized = smart contracts, users keep own keys

Centralized: counterparty risk. Decentralized: smart contract risk.

Custody models

Self-custody = owner holds keys | Third-party custody = custodian holds keys

Third-party custody shifts key-management risk but adds counterparty risk.

Tokenization

Real or financial asset → digital token on a ledger representing ownership

Benefits: fractional ownership, faster settlement, transparency. The token is a claim, not the asset itself.

Smart contract logic

If predefined condition is met → code executes automatically

Runs without intermediary, but code errors can be irreversible.

Holding period return (price only)

HPR = (P₁ − P₀) ÷ P₀

Use for assets with no income. Add any staking or lending income to the numerator if it is paid.

Holding period return (with income)

HPR = (P₁ − P₀ + Income) ÷ P₀

Income may be staking rewards or lending interest. If rewards are paid in additional tokens, either value them at year-end and treat them as income, or include them in the ending value, but not both.

Cost-of-production anchor

Approximate floor value per unit ≈ Total cost of producing units ÷ Number of units produced

A rough guide for mined assets. Market price can stay above or below it.

Network-usage valuation idea

Value per token ≈ Value of network activity ÷ Number of tokens

A conceptual comparison method, not a formula with one accepted form. Treat results with caution.

Portfolio variance of two assets

σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁₂σ₁σ₂

Shows why low correlation (ρ) helps diversification even for a very volatile asset held in a small weight.

Quick revision

• DLT is a shared database kept in sync across many participants without a single central owner.
• Consensus is how network participants agree on the valid state of the ledger.
• Cryptography secures records and proves ownership through keys.
• Permissionless networks are open to anyone; permissioned networks restrict who may participate or validate.
• Permissioned networks trade openness for more control and privacy.
• Stablecoins aim to hold a stable value by referencing another asset, and the quality of that backing is the key risk.
• Tokenization represents rights in an asset as a digital token on a ledger.
• Custody risk comes from holding or losing the keys that control the asset.
• Exchanges, custodians and wallets are core pieces of market infrastructure.
• Many digital assets have no cash flows, so valuation is harder and relies on other approaches.
• Regulatory and operational risks can be as important as price volatility.
• Pick the answer that matches the definition, and avoid options with absolute claims.

Common mistakes

• Treating DLT and blockchain as the same thing. Fix: Remember that blockchain is one type of DLT. DLT is the broader idea of a shared, synchronized ledger.
• Swapping the features of proof of work and proof of stake. Fix: Link PoW to computing power and energy cost, and PoS to locked coins that can be forfeited.
• Treating a CBDC as a cryptocurrency. Fix: Look at the issuer. A CBDC is issued by a central bank and is centrally controlled. Cryptocurrencies have no central issuer.
• Assuming every stablecoin is fully backed and risk-free. Fix: Stability depends on the backing and redemption ability. The peg can fail.
• Treating permissionless as meaning no rules at all. Fix: Permissionless means no approval is needed to join. Consensus rules still govern what is valid.
• Assuming permissioned networks are not blockchains or are not decentralized at all. Fix: Permissioned networks are still distributed ledgers, just with restricted participation and more centralized governance.
• Saying a wallet holds the coins. Fix: Remember that assets sit on the ledger. The wallet stores the keys that control them.
• Treating cold wallets as risk-free. Fix: Cold storage reduces hacking risk but adds risk of loss, theft of the device or forgotten keys.
• Applying a dividend discount model to a cryptocurrency with no cash flows. Fix: Ask first whether the asset pays anything. If not, use cost of production, network usage or comparables, and say valuation is uncertain.
• Assuming digital assets always diversify a portfolio. Fix: Remember correlation can change and may rise in market stress. Diversification benefit is possible, not guaranteed.

Exam tips

• Expect comparison questions: PoW versus PoS, distributed ledger versus central ledger, public key versus private key.
• Read for the single clue word, such as 'energy', 'stake' or 'secret', and match it to one concept before looking at the options.
• Treat extreme wording, such as 'eliminates all risk', as a warning sign, since DLT reduces some risks but not all.
• Keep definitions short. If you can state each term in one sentence, you can usually remove two options fast.
• This topic needs no calculator. Save your time for numerical questions elsewhere.
• Most questions test the issuer and the claim. Find those two facts first.
• Watch for stems that describe a peg and then ask which asset it is. That is a stablecoin.
• Do not confuse access rights (utility) with ownership rights (security).