Free lesson · Markets & returns

Translate an investment idea into a mandate

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Start with the idea

A mandate converts an investment story into observable boundaries. A low net exposure can conceal large offsetting positions; those positions still consume financing, liquidity and attention. Separate economic exposures from the constraints used to manage them.

Symbols, units & horizon

MVᵢ: signed market value of position i
NAV: positive net asset value
wᵢ: position weight MVᵢ/NAV
G: gross exposure as a fraction of NAV
N: net exposure as a fraction of NAV
L: sum of positive weights
S: magnitude of negative weights
| |: absolute value
Σᵢ: sum over positions

When and why to use this

Use signed weights when constructing a book and gross exposure when monitoring financing and liquidation demands. Use the written mandate to decide whether a proposed signal belongs in the fund at all.

A fund mandate specifies what the portfolio is allowed to do and what success means. Start with an economic mechanism: who pays the expected return, why the opportunity persists, and which conditions make it disappear. A profitable historical pattern alone does not answer those questions.

Universe and horizon: specify instruments, market hours, holding periods, currencies, and eligible counterparties.
Objective and benchmark: distinguish absolute return, market-relative return, capital preservation, and liability matching.
Constraints: gross and net exposure, concentration, liquidity, borrow, derivatives, and cash reserves.
Decision record: state what would invalidate the thesis and who can reduce or stop trading.

gross = \sum_{i} | w_{i} |, net = \sum_{i} w_{i}, w_{i} = \frac{{s i g n e d m a r k e t v a l u e}_{i}}{N A V}

Algebra and arithmetic

Normalise positions and separate gross from net

Divide each signed market value by NAV: $w_{i} = \frac{M V_{i}}{N A V}$ . Adding without signs lost gives net exposure; adding absolute values gives gross exposure.
If long exposure L and short magnitude S are nonnegative, $G = L + S$ and $N = L - S$ . Add the equations to solve $L = \frac{(G + N)}{2}$ ; subtract to get $S = \frac{(G - N)}{2}$ .

Work it by hand

A $10m NAV with $12m long and $8m short has weights +1.2 and −0.8, gross 2.0 and net 0.4. Conversely G=2, N=.4 implies L=1.2 and S=.8.

An equity book 120% long and 80% short has 200% gross and 40% net exposure. Net exposure can be small while sector, volatility, financing, or crowded-position risk remains large. These market-value measures need additional risk equivalents for derivatives.

Research sources, review dates and limitations

Extend the research question

Compare spot ownership, a dated future and a perpetual on the same underlying. Identify who holds collateral, when cash moves and which contract convention changes the payoff.

Continue with the connected research module →

Connect the ideas: Cash flows and accounting

Retrieve: Track units, signed cash movements and ownership at each event.

Check the change: Instrument obligations, financing and external capital flows change the ledger you need.

Math & notation → Trading different assets → Research & backtests → Execution & microstructure → Fund operations & capstone → Putting it all together

Explain it yourself: Why can an account balance rise without an investment profit?

Self-assessed. Write your explanation before opening this comparison.

A deposit raises the balance without being investment P&L. Reconcile external flows separately from fills, fees and marked holdings.

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def exposures(market_values, nav):
    if nav <= 0:
        raise ValueError("Positive NAV required")
    weights = [value/nav for value in market_values]
    return sum(abs(w) for w in weights), sum(weights)

def long_short(gross, net):
    if gross < abs(net):
        raise ValueError("Gross cannot be smaller than absolute net")
    return (gross+net)/2, (gross-net)/2

print(exposures([12e6, -8e6], 10e6), long_short(2, .4))

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