Basket Return and Dollar P&L Calculation
You are running a 3-name basket with weights $(0.50, 0.30, 0.20)$. Over the last minute, the three names moved by $+1.20\%$, $-0.60\%$, and $+0.15\%$ respectively. The basket notional is $\$2{,}000{,}000$.
(a) What is the basket return in basis points?
(b) What is the dollar P&L on the basket?
Hints
- The basket return is the weighted average of the individual name returns: $R = \sum w_i R_i$.
- Do the dominant term first: the 50% weight on the +1.20% name contributes 60 bps. The other terms are corrections of -18 bps and +3 bps.
- Once you have the percentage return, dollar P&L = (return as decimal) $\times$ notional. A 45 bp move on $2M is $0.0045 \times 2{,}000{,}000$.
Worked Solution
How to Think About It: This is pure mental math -- a trader should be able to do this in under 30 seconds. The basket return is just a weighted average of the individual returns. Then multiply by the notional to get the dollar move. Do the weights times returns in your head: the 50% weight on the +1.20% name is the dominant driver.
Quick Estimate: $0.5 \times 1.20 = 0.60$. The other two are small corrections: $0.3 \times (-0.60) = -0.18$ and $0.2 \times 0.15 = 0.03$. Total: $0.60 - 0.18 + 0.03 = 0.45\%$. That is 45 bps. Dollar P&L: $0.0045 \times 2{,}000{,}000 = \$9{,}000$.
Approach: Weighted sum of individual returns gives the portfolio return. Dollar P&L = portfolio return times notional.
Formal Solution:
(a) Basket return:
$$R_{\text{basket}} = \sum_{i=1}^{3} w_i R_i = 0.50 \times (+1.20\%) + 0.30 \times (-0.60\%) + 0.20 \times (+0.15\%)$$
$$= 0.60\% - 0.18\% + 0.03\% = 0.45\%$$
Converting to basis points (1 bp = 0.01%): $$R_{\text{basket}} = \boxed{45 \text{ bps}}$$
(b) Dollar P&L:
$$\Delta V = R_{\text{basket}} \times \text{Notional} = 0.0045 \times \$2{,}000{,}000 = \boxed{\$9{,}000}$$
Answer: The basket returned 45 bps and the dollar P&L was $9,000.
Intuition
Weighted portfolio returns are additive -- the basket return is just the dot product of your weight vector and the return vector. This linearity is the foundation of almost everything in portfolio math: it means you can decompose risk and P&L by position, hedge positions independently, and compute portfolio-level statistics from position-level ones.
In practice, traders constantly do this calculation in their heads. The skill is learning to identify the dominant term quickly (here, the 50%-weighted position doing +120 bps) and treating the rest as small corrections. Getting comfortable with the '1 bp on $1M = $100' conversion is also essential: 45 bps on $2M is $90 per bp times 100 bps, or equivalently $100 per bp on $1M times 45 bps times 2 = $9,000.