First commit

.gitignore

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+*node_modules/
+*yarn-error.log*
+*.orig
+
+# Swap
+[._]*.s[a-v][a-z]
+[._]*.sw[a-p]
+[._]s[a-rt-v][a-z]
+[._]ss[a-gi-z]
+[._]sw[a-p]
+

.prettierrc

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+{
+    "trailingComma": "all",
+    "tabWidth": 4,
+    "printWidth": 80,
+    "arrowParens": "avoid"
+}

README.md

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+Quick attempt at an optimal portfolio balancer.
+
+##Notes: 
+1. The balancing algorithm is not currently optimal (Work in progress). [See Closeness section](#closeness)
+1. No external stock API is used. The given API gives only daily time-series output. This application is built as a stream processing system which would allow automatic rebalancing for specific events such as a price change of more than X%. I may add a randomized price generator as an input.
+
+## Install
+```
+yarn
+```
+
+## To run
+Using the pre-seed file with pricing from Jul 12th:
+```
+< test node .
+```
+
+Using the pre-seed file and allowing interactive commands:
+```
+cat test - | node .
+```
+
+
+## Interactive Commands:
+`
+<TICKER>:<price>
+`
+Sets the stock price for the given ticker
+
+example:
+```
+AAPL:152.3
+```
+
+`
+rebalance:<account_id>
+`
+Triggers a rebalance for the given account ID
+
+example:
+```
+rebalance:1
+```
+note: Account 1 is there by default.
+
+
+## Closeness
+
+The problem of portfolio balancing can be described as such:
+```
+Minimize:
+   w_f - w_t
+   e.g.
+      SUM( |c_i*p_i - t_i| ) for stocks i
+   or
+      SUM( (c_i*p_i - t_i)^2 ) for stocks i
+
+Subject to:
+   SUM( c_i*p_i ) <= T
+   c_i are Integers >= 0
+
+Where
+   w_f is the final portfolio
+   w_t is the target portfolio
+   c_i is the number of shares of stock i
+   p_i is the price of stock i
+   t_i is the total optimal fractional amount invested in stock i
+      e.g. % allocation * total portfolio value
+```
+
+This problem statement falls in the Mixed Integers Quadratic Programming category. This problem can be solved through enumeration in exponential time `2^n` where n is the total
+number of possible stocks purchase (not just ticker), which is very much impractical. Optimisations can be applied to reduce it to `2^n` where n is the total number of tickers,
+although still exponential. From there (or possibly through a simplified problem statement), this can possibly be solved in pseudo-polynomial time using algorithms such as
+branch-and-bound or Quadknap.
+
+Currently, the algorithm used is non-optimal in some edge-cases but produces very close results in most cases. That algorithm runs in linear time (quasilinear if tickers are not
+previously sorted) and can be used to evaluate the bounds in a branch-and-bound algorithm for potentially optimal results.
+
+Unfortunately, time constraints prevented me from finishing the implementation as of Sunday July 12th. I will update this README if that changes.

package.json

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+{
+  "name": "portfolio-blancer",
+  "version": "1.0.0",
+  "main": "index.js",
+  "author": "Lewis Diamond",
+  "license": "MIT",
+  "dependencies": {
+    "strom": "ssh://git@git.lewis.id:ldiamond/strom.git",
+    "uuid": "^8.2.0"
+  },
+  "devDependencies": {
+    "ava": "^3.9.0",
+    "prettier": "^2.0.5"
+  },
+  "scripts": {
+    "test": "ava",
+    "test:debug": "node inspect node_modules/ava/profile.js"
+  },
+  "main": "src/index.js"
+}

src/index.js

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+const strom = require("strom").strom();
+const { allInUSD } = require("./pure/balancer");
+const REBALANCE = "rebalance";
+const PRICING = "pricing";
+//Pricing as of July 12th;
+const SEED = {
+    AAPL: 383.68,
+    GOOG: 1541.74,
+    ACAD: 55.45,
+    GFN: 6.23,
+    CYBR: 109.0,
+    ABB: 24.49,
+};
+const pricingStore = require("./stores/pricing").global({ seed: SEED });
+const pricing = require("./processors/pricing")();
+const balancer = require("./processors/balancer")();
+
+//Conversion layer for manual input
+const stdinReader = strom.compose([
+    strom.split(),
+    strom.map(data => data.trim()),
+    strom.filter(str => !!str),
+    strom.map(str => {
+        const [cmd, param] = str.split(":");
+        switch (cmd) {
+            case REBALANCE:
+                return { type: REBALANCE, accountId: param };
+            default:
+                return { type: PRICING, ticker: cmd, price: param };
+        }
+    }),
+]);
+
+//This pipeline could be built in a configurable way such that the input is
+//either stdin + interactive, stdin as JSON/protobuff, a Kafka topic, a NATS
+//topic, a RabbitMQ topic, a file, etc.
+process.stdin
+    //The conversion layer would be added conditionally
+    .pipe(stdinReader)
+    .pipe(
+        strom.demux(key => {
+            switch (key) {
+                case REBALANCE:
+                    return balancer;
+                    break;
+                case PRICING:
+                    return pricing;
+                    break;
+            }
+        }, "type"),
+    )
+    //This is logging for presentation only. This could also be a module added
+    //conditionally.
+    .pipe(
+        strom.map(data => {
+            const { account, balanced, actions, pricing } = data;
+            if (account && balanced && actions && pricing) {
+                const balancedValue = allInUSD(balanced, pricing);
+                const previousValue = allInUSD(account.openPositions, pricing);
+                console.log("Previous positions");
+                console.table(account.openPositions);
+                console.log("Balanced portfolio");
+                console.table(balanced);
+                console.log("Transactions required");
+                const transactionsPivot = Array.from(
+                    new Set(Object.keys({ ...actions.buy, ...actions.sell })),
+                ).reduce((acc, ticker) => {
+                    acc[ticker] = {
+                        buy: actions.buy[ticker] || 0,
+                        sell: actions.sell[ticker] || 0,
+                    };
+                    return acc;
+                }, {});
+                console.table(transactionsPivot);
+                console.log("Total value");
+                console.table({
+                    balanced: balancedValue,
+                    previous: previousValue,
+                });
+
+                console.table(
+                    Object.entries(account.targets).reduce(
+                        (acc, [ticker, target]) => {
+                            const price = pricing[ticker];
+                            acc[ticker] = {
+                                target,
+                                balanced:
+                                    (balanced[ticker] * price) / previousValue,
+                                previous:
+                                    (account.openPositions[ticker] * price) /
+                                    previousValue,
+                            };
+                            return acc;
+                        },
+                        {},
+                    ),
+                );
+            }
+            return data;
+        }),
+    )
+    .pipe(strom.map(out => console.log(JSON.stringify(out))));

src/processors/balancer.js

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+const strom = require("strom").strom();
+const account = require("../stores/account");
+const pricing = require("../stores/pricing");
+const { balance, portfolioDiff, allInUSD } = require("../pure/balancer");
+
+module.exports = function ({
+    accounts = undefined,
+    accountStore = account({ accounts }),
+    pricingStore = pricing.global(),
+} = {}) {
+    return strom.compose([
+        strom.map(({ accountId }) => {
+            try {
+                const account = accountStore.get(accountId);
+                const { openPositions, targets } = account;
+                const pricing = pricingStore.subset(
+                    ...Object.keys(openPositions),
+                    ...Object.keys(targets),
+                );
+
+                const balanced = balance(openPositions, targets, pricing);
+                return { account, balanced, pricing };
+            } catch (e) {
+                console.error(e);
+                console.error("Invalid rebalance command or invalid accountId");
+            }
+        }),
+        strom.map(({ account, balanced, pricing }) => {
+            const actions = {
+                accountId: account.id,
+                ...portfolioDiff(account.openPositions, balanced),
+            };
+            accountStore.setOpenPositions(account.id, balanced);
+            return { account, balanced, pricing, actions };
+        }),
+    ]);
+};

src/processors/balancer.spec.js

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+const test = require("ava");
+const strom = require("strom");
+const { map, fromArray, collect, collected } = strom.strom();
+const uuidv4 = require("uuid/v4");
+const PricingStore = require("../stores/pricing");
+const Balancer = require("./balancer");
+
+test.beforeEach(t => {
+    //Pricing as of July 12th;
+    const pricingCache = {
+        AAPL: 383.68,
+        GOOG: 1541.74,
+        ACAD: 55.45,
+        GFN: 6.23,
+        CYBR: 109.0,
+        ABB: 24.49,
+    };
+    const accountId = uuidv4();
+    const accounts = {
+        [accountId]: {
+            id: accountId,
+            openPositions: {
+                AAPL: 50,
+                GOOG: 200,
+                CYBR: 150,
+                ABB: 900,
+                USD: 0,
+            },
+            targets: {
+                AAPL: 0.22,
+                GOOG: 0.38,
+                GFN: 0.25,
+                ACAD: 0.15,
+                USD: 0,
+            },
+        },
+    };
+    const pricingStore = PricingStore.instance({ cache: pricingCache });
+    const balancer = Balancer({ accounts, pricingStore });
+    t.context = {
+        balancer,
+        pricingStore,
+        pricingCache,
+        accountId,
+        accounts,
+    };
+});
+test("Accounts are read, pricing is obtained and a balanced account is derived", async t => {
+    const {
+        balancer,
+        accountStore,
+        accounts,
+        accountId,
+        pricingStore,
+    } = t.context;
+
+    const account = accounts[accountId];
+    const result = await strom.collected(
+        fromArray([{ accountId }]).pipe(balancer).pipe(collect()),
+    );
+    t.deepEqual(result, [
+        {
+            account,
+            balanced: {
+                AAPL: 210,
+                GOOG: 90,
+                GFN: 14703,
+                ACAD: 991,
+                USD: 42.959999999984575,
+            },
+            actions: {
+                accountId,
+                buy: {
+                    AAPL: 160,
+                    ACAD: 991,
+                    GFN: 14703,
+                    USD: 42.959999999984575,
+                },
+                sell: {
+                    GOOG: 110,
+                    CYBR: 150,
+                    ABB: 900,
+                },
+            },
+            pricing: pricingStore.subset(
+                ...Object.keys(account.openPositions),
+                ...Object.keys(account.targets),
+            ),
+        },
+    ]);
+});
+
+test("No order will be sent without pricing data on all relevant titles", async t => {
+    const {
+        balancer,
+        accountStore,
+        accounts,
+        accountId,
+        pricingStore,
+    } = t.context;
+
+    pricingStore.set("AAPL", 0);
+    const result = await strom.collected(
+        fromArray([{ accountId }]).pipe(balancer).pipe(collect()),
+    );
+
+    t.deepEqual(result, []);
+});

src/processors/pricing.js

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+const strom = require("strom").strom();
+const pricing = require("../stores/pricing");
+
+module.exports = function ({
+    seed = undefined,
+    pricingStore = pricing.global({ seed }),
+} = {}) {
+    return strom.map(({ ticker, price }) => {
+        if (price) {
+            pricingStore.set(ticker, parseFloat(price));
+        }
+        console.log(`Pricing for ${ticker} set to ${pricingStore.get(ticker)}`);
+        return;
+    });
+};

src/pure/balancer.js

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+const USD = "USD";
+function allInUSD(openPositions, pricing) {
+    return Object.entries(openPositions).reduce((acc, [ticker, amnt]) => {
+        const price = pricing[ticker];
+        //0, undefined and any falsy value should throw
+        if (!price) {
+            throw new Error(
+                `Can't get portfolio value because of missing pricing information on ${ticker}`,
+            );
+        }
+        return acc + price * amnt;
+    }, 0);
+}
+
+/*
+ * Takes a portfolio and the total value and returns the amount of USD available
+ */
+function leftOverCash(positions, value, pricing) {
+    return (
+        Object.entries(positions).reduce(
+            (acc, [k, v]) => acc - v * pricing[k],
+            value,
+        ) + (positions.USD || 0)
+    );
+}
+
+/*
+ * This function rounds half away from infinity
+ * That is:
+ *  5.5 -> 5
+ *  -5.5 -> -6
+ */
+function roundHAFI(number) {
+    return -Math.round(-number);
+}
+
+function balance(openPositions, targetPositions, pricing, algo = round) {
+    const value = allInUSD(openPositions, pricing);
+    const balanced = algo(targetPositions, value, pricing);
+    return balanced.result;
+}
+
+/* Takes the target positions, portfolio value and pricing and returns the
+ * optimal stock allocation with no integer requirement
+ */
+function optimalFractional(targetPositions, value, pricing) {
+    return Object.fromEntries(
+        Object.entries(targetPositions).map(([k, v]) => [
+            k,
+            (v * value) / pricing[k],
+        ]),
+    );
+}
+
+/* Non-optimal (but linear-time) function to get ticker quantities based on
+ * target positions, pricing and total portfolio value s.t.
+ * SUM(c_1*p_1 + c_2*p_2 + ... + c_i*p_i) <= T
+ * AND
+ *  c_i*p_i <= t_i * T for i in t [excluding USD]
+ * WHERE
+ *  c_i is the number of share of i
+ *  p_i is the value of a share of i
+ *  T is the total value of the portfolio
+ *  t_i is the target allocation (in decimal %, e.g. 0.22 for 22%)
+ *  t in the target allocations
+ *
+ */
+function floor(targetPositions, value, pricing) {
+    const positions = Object.fromEntries(
+        Object.entries(targetPositions).map(([ticker, target]) => [
+            ticker,
+            Math.floor((target * value) / pricing[ticker]),
+        ]),
+    );
+    positions.USD = leftOverCash(positions, value, pricing);
+    return {
+        result: positions,
+        diff: difference(positions, targetPositions, value, pricing),
+    };
+}
+
+/* Non-optimal (but linear-time/quasilinear) function to get ticker quantities
+ * based on target positions, pricing and total portfolio value
+ * s.t.
+ * SUM(c_1*p_1 + c_2*p_2 + ... + c_i*p_i) <= T
+ * and minimizes USD
+ * WHERE
+ *  c_i is the number of share of i
+ *  p_i is the value of a share of i
+ *  T is the total value of the portfolio
+ *  t_i is the target allocation (in decimal %, e.g. 0.22 for 22%)
+ *  t in the target allocations
+ *
+ */
+function round(targetPositions, value, pricing) {
+    //Descending order
+    const sortedPricing = Object.entries(targetPositions)
+        .filter(([x]) => x !== USD)
+        .sort(([, p1], [, p2]) => p2 - p1);
+
+    const final = sortedPricing.reduce(
+        (acc, [ticker], idx) => {
+            const { result, cash, remaining } = acc;
+            const price = pricing[ticker];
+            const targetTicker = targetPositions[ticker];
+            const optimalQty = (cash * (targetTicker / acc.remaining)) / price;
+            const roundQty = Math.round(optimalQty);
+            const floorQty = Math.floor(optimalQty);
+            const qty = roundQty * price <= cash ? roundQty : floorQty;
+            result[ticker] = qty;
+            acc.cash -= qty * price;
+            acc.remaining -= targetTicker;
+            return acc;
+        },
+        { result: {}, cash: value, remaining: 1 },
+    );
+    final.result.USD = final.cash;
+    return {
+        result: final.result,
+        diff: difference(final.result, targetPositions, value, pricing),
+    };
+}
+
+/*
+ * Optimal solution using enumeration, exponential time-complexity.
+ *
+ * Minimizes SUM( ABS(c_i * p_i - T * t_i) ) for i in t
+ * Subject to:
+ *  SUM( c_i*p_i ) = T
+ *  c_i is Integer (except for USD)
+ */
+function enumeration(targetPositions, value, pricing) {
+    const optimal = optimalFractional(targetPositions, value, pricing);
+    const zero = Object.entries(targetPositions).reduce(
+        (acc, [k, v]) => ({
+            [k]: 0,
+            ...acc,
+        }),
+        { USD: value },
+    );
+    const best = Infinity;
+
+    const optimize = (positions, state) => {
+        if (positions.length === 0) {
+            const leftOver = leftOverCash(state, value, pricing);
+            const result = leftOver >= 0 ? { ...state, USD: leftOver } : zero;
+            return {
+                result,
+                diff: difference(result, targetPositions, value, pricing),
+            };
+        }
+        const currentTicker = positions.pop();
+        const currentAlloc = optimal[currentTicker];
+        const left = optimize([...positions], {
+            ...state,
+            [currentTicker]: Math.floor(currentAlloc),
+        });
+        const right = optimize([...positions], {
+            ...state,
+            [currentTicker]: Math.ceil(currentAlloc),
+        });
+
+        if (right.diff == left.diff) {
+            return right.result.USD >= left.result.USD ? left : right;
+        } else {
+            return right.diff >= left.diff ? left : right;
+        }
+    };
+
+    return optimize(Object.keys(targetPositions), {});
+}
+
+/*
+ * Optimal solution using branch-and-bound, ? time-complexity.
+ *
+ * This essentially enumerates all solitions but improves performance by
+ * skipping branches that can't possibly lead to a better result than already
+ * found.
+ *
+ * Minimizes SUM( ABS(c_i * p_i - T * t_i) ) for i in t
+ * Subject to:
+ *  SUM( c_i*p_i ) = T
+ *  c_i is Integer (except for USD)
+ */
+function branchAndBound(targetPositions, value, pricing) {
+    const optimal = optimalFractional(targetPositions, value, pricing);
+    const { diff: floorDiff } = floor(targetPositions, value, pricing);
+    const zero = {
+        result: Object.entries(targetPositions).reduce(
+            (acc, [k, v]) => ({
+                [k]: 0,
+                ...acc,
+            }),
+            { USD: value },
+        ),
+        diff: Infinity,
+    };
+    let best = floorDiff;
+
+    const optimize = state => {
+        const currentNode = { ...optimal, ...state };
+        const [bindTicker, bindCount] =
+            Object.entries(currentNode)
+                .sort(
+                    ([ticker], [ticker2]) => pricing[ticker2] - pricing[ticker],
+                )
+                .find(([ticker, count]) => ticker !== USD && count % 1 !== 0) ||
+            [];
+
+        if (bindTicker) {
+            let left = {
+                ...currentNode,
+                [bindTicker]: Math.floor(bindCount),
+            };
+            let right = {
+                ...currentNode,
+                [bindTicker]: Math.ceil(bindCount),
+            };
+
+            const diffLeft = difference(left, targetPositions, value, pricing);
+            const diffRight = difference(
+                right,
+                targetPositions,
+                value,
+                pricing,
+            );
+
+            left = diffLeft < best ? optimize(left) : zero;
+            right = diffRight < best ? optimize(right) : zero;
+
+            return left.diff <= right.diff ? left : right;
+        } else {
+            //All are integers, we're done with this branch
+            const leftOver = leftOverCash(currentNode, value, pricing);
+            const final = {
+                ...currentNode,
+                [USD]: leftOver,
+            };
+            const feasible = allInUSD(final, pricing) <= value && leftOver >= 0;
+            const diff = difference(final, targetPositions, value, pricing);
+            best = diff < best && feasible ? diff : best;
+            return feasible && leftOver >= 0
+                ? {
+                      result: final,
+                      diff,
+                  }
+                : zero;
+        }
+    };
+
+    return optimize({});
+}
+
+/* Computes the sum of the absolute difference to target value
+ */
+function difference(
+    positions,
+    targetPositions,
+    value,
+    pricing,
+    ignoreUSD = false,
+) {
+    //All keys from positions and targetPositions are the same.
+    return Object.entries(positions)
+        .filter(([ticker]) => !ignoreUSD || ticker !== USD)
+        .map(([ticker, count]) =>
+            Math.abs(count * pricing[ticker] - value * targetPositions[ticker]),
+        )
+        .reduce((acc, v) => acc + v, 0);
+}
+
+function simplex(targetPositions, value, locked) {}
+
+function portfolioDiff(openPositions, finalPositions) {
+    const ret = { sell: {}, buy: {} };
+    const tickers = new Set([
+        ...Object.keys(openPositions),
+        ...Object.keys(finalPositions),
+    ]);
+    tickers.forEach(ticker => {
+        const n = (finalPositions[ticker] || 0) - (openPositions[ticker] || 0);
+        if (n < 0) {
+            ret.sell[ticker] = -n;
+        } else if (n > 0) {
+            ret.buy[ticker] = n;
+        }
+    });
+    return ret;
+}
+
+module.exports = {
+    floor,
+    round,
+    balance,
+    leftOverCash,
+    allInUSD,
+    enumeration,
+    difference,
+    optimalFractional,
+    branchAndBound,
+    portfolioDiff,
+};

src/pure/balancer.spec.js

@@ -0,0 +1,380 @@
+const test = require("ava");
+const {
+    allInUSD,
+    balance,
+    floor,
+    leftOverCash,
+    round,
+    enumeration,
+    difference,
+    optimalFractional,
+    branchAndBound,
+} = require("./balancer");
+const almostEqual = (n1, n2, d = 0.000001) => {
+    return Math.abs(n1 - n2) <= d;
+};
+
+const REAL_CASE = {
+    //Pricing as of July 12th;
+    pricing: {
+        AAPL: 383.68,
+        GOOG: 1541.74,
+        ACAD: 55.45,
+        GFN: 6.23,
+        CYBR: 109.0,
+        ABB: 24.49,
+        USD: 1,
+    },
+    openPositions: {
+        AAPL: 50,
+        GOOG: 200,
+        CYBR: 150,
+        ABB: 900,
+        USD: 0,
+    },
+    targets: {
+        AAPL: 0.22,
+        GOOG: 0.38,
+        GFN: 0.25,
+        ACAD: 0.15,
+        USD: 0,
+    },
+};
+
+test("Balance takes a portfolio and returns the balanced result based on the given algorithm", t => {
+    const { pricing, openPositions, targets } = REAL_CASE;
+    const value = allInUSD(openPositions, pricing);
+    const floored = balance(openPositions, targets, pricing, floor);
+    const enumerated = balance(openPositions, targets, pricing, enumeration);
+    const bnb = balance(openPositions, targets, pricing, branchAndBound);
+    const rounded = balance(openPositions, targets, pricing, round);
+
+    const expectedFloor = {
+        AAPL: 209,
+        GOOG: 90,
+        GFN: 14683,
+        ACAD: 989,
+        USD: 662.1399999999849,
+    };
+
+    t.deepEqual(floored, expectedFloor);
+
+    //The portfolio value does not change.
+    t.true(almostEqual(allInUSD(enumerated, pricing), value), "Enumeration");
+    const optimalDiff = difference(enumerated, targets, value, pricing);
+
+    //Floored
+    t.is(allInUSD(floored, pricing), value);
+
+    //Rounded
+    //In this case, we get an optimal result
+    t.true(almostEqual(allInUSD(rounded, pricing), value));
+    t.true(
+        almostEqual(optimalDiff, difference(rounded, targets, value, pricing)),
+    );
+
+    //Branch and bound
+    t.true(almostEqual(allInUSD(rounded, pricing), value));
+    t.true(
+        almostEqual(optimalDiff, difference(rounded, targets, value, pricing)),
+    );
+});
+
+test("floor -- Simple balancing", t => {
+    const pricing = {
+        AAPL: 1000,
+        GOOG: 500,
+        GFN: 200,
+        ACAD: 110,
+        USD: 1,
+    };
+
+    const targets = {
+        AAPL: 0.22,
+        GOOG: 0.38,
+        GFN: 0.25,
+        ACAD: 0.15,
+        USD: 0,
+    };
+
+    const value = 25000;
+    const expected = {
+        AAPL: 5,
+        GOOG: 19,
+        GFN: 31,
+        ACAD: 34,
+    };
+    expected.USD = leftOverCash(expected, value, pricing);
+    const floored = floor(targets, value, pricing);
+    t.deepEqual(floored.result, expected);
+});
+
+test("floor -- can't allocate a stock if the target allocation is below the ticker price", t => {
+    const pricing = {
+        AAPL: 1000,
+        GOOG: 500,
+        GFN: 200,
+        ACAD: 110,
+        USD: 1,
+    };
+
+    const targets = {
+        AAPL: 0.22,
+        GOOG: 0.38,
+        GFN: 0.25,
+        ACAD: 0.15,
+        USD: 0,
+    };
+
+    const value = 4000;
+    const expected = {
+        AAPL: 0,
+        GOOG: 3,
+        ACAD: 5,
+        GFN: 5,
+    };
+    expected.USD = leftOverCash(expected, value, pricing);
+    const floored = floor(targets, value, pricing);
+    t.deepEqual(floored.result, expected);
+});
+
+test("all -- a USD position is not rounded", t => {
+    const pricing = {
+        AAPL: 4.103775,
+        GOOG: 4.103775,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.4103775,
+        GOOG: 0.4103775,
+        USD: 0.179245,
+    };
+    const value = 10;
+    const floored = floor(targets, value, pricing);
+    const rounded = round(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+    const optimal = enumeration(targets, value, pricing);
+
+    const resultUSD = 1.7924500000000005;
+    t.true(almostEqual(floored.result.USD, resultUSD));
+    t.true(almostEqual(rounded.result.USD, resultUSD));
+    t.true(almostEqual(bnb.result.USD, resultUSD));
+    t.true(almostEqual(optimal.result.USD, resultUSD));
+});
+
+test("round,enumeration,branchAndBound -- A USD target position is respected", t => {
+    const pricing = {
+        AAPL: 10,
+        GOOG: 10,
+        USD: 1,
+    };
+
+    const targets = {
+        AAPL: 0.6,
+        GOOG: 0.3,
+        USD: 0.1,
+    };
+
+    const value = 100;
+    const rounded = round(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+
+    t.is(rounded.result.USD, 10);
+    t.is(enumerated.result.USD, 10);
+    t.is(bnb.result.USD, 10);
+    t.is(allInUSD(rounded.result, pricing), 100);
+    t.is(allInUSD(enumerated.result, pricing), 100);
+    t.is(allInUSD(bnb.result, pricing), 100);
+});
+
+test("round,enumeration,branchAndBound -- A USD target position is respected #2 ", t => {
+    const pricing = {
+        AAPL: 10,
+        GOOG: 16,
+        USD: 1,
+    };
+
+    const targets = {
+        AAPL: 0.6,
+        GOOG: 0.3,
+        USD: 0.1,
+    };
+
+    const value = 100;
+    const rounded = round(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+
+    t.is(rounded.result.USD, 8);
+    t.is(enumerated.result.USD, 8);
+    t.is(bnb.result.USD, 8);
+});
+
+test("Rounding - rounding up a stock doesn't over-commit available capital", t => {
+    const pricing = {
+        AAPL: 100,
+        GOOG: 10,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.51,
+        GOOG: 0.49,
+        USD: 0,
+    };
+
+    const value = 99;
+    const rounded = round(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+    const _enum = enumeration(targets, value, pricing);
+    t.true(rounded.result.USD >= 0);
+    t.true(bnb.result.USD >= 0);
+    t.true(_enum.result.USD >= 0);
+    t.is(rounded.result.AAPL, 0);
+    t.is(bnb.result.AAPL, 0);
+    t.is(_enum.result.AAPL, 0);
+
+    t.is(allInUSD(rounded.result, pricing), value);
+    t.is(allInUSD(bnb.result, pricing), value);
+    t.is(allInUSD(_enum.result, pricing), value);
+
+    t.is(_enum.diff, rounded.diff);
+    t.is(_enum.diff, bnb.diff);
+});
+
+test("Can't buy a stock that is too expensive", t => {
+    const pricing = {
+        AAPL: 10,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 1,
+        USD: 0,
+    };
+    const value = 5;
+    const floored = floor(targets, value, pricing);
+    const rounded = round(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+
+    t.is(floored.result.AAPL, 0);
+    t.is(floored.result.USD, 5);
+    t.is(rounded.result.AAPL, 0);
+    t.is(rounded.result.USD, 5);
+    t.is(enumerated.result.AAPL, 0);
+    t.is(enumerated.result.USD, 5);
+    t.is(bnb.result.AAPL, 0);
+    t.is(bnb.result.USD, 5);
+});
+
+test("Rounding up would have negative consequences on portfolio closeness -- <0.5 allocation + highest price rounded", t => {
+    const value = 1100;
+    const pricing = {
+        AAPL: 1000,
+        GOOG: 561,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.49,
+        GOOG: 0.51,
+        USD: 0,
+    };
+    const rounded = round(targets, value, pricing);
+    const floored = floor(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    t.is(rounded.result.GOOG, 1);
+    t.is(floored.result.GOOG, 1);
+    t.is(bnb.result.GOOG, 1);
+    t.is(enumerated.result.GOOG, 1);
+    t.true(almostEqual(allInUSD(rounded.result, pricing), value));
+    t.true(almostEqual(allInUSD(floored.result, pricing), value));
+    t.true(almostEqual(allInUSD(bnb.result, pricing), value));
+    t.true(almostEqual(allInUSD(enumerated.result, pricing), value));
+});
+
+//This proves that a portfolio where all positions are less than 1 unit away
+//from the fractional optimal (i.e. rounded up or down) are not always the
+//optimal integer values.
+test.skip("Optimal result may be achieved by more than rounding (remove more than 1 stock from fractional)", t => {
+    const value = 1100;
+    const pricing = {
+        AAPL: 1000,
+        GOOG: 269.5,
+        TSLA: 1,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.49,
+        GOOG: 0.255,
+        TSLA: 0.255,
+        USD: 0,
+    };
+    const rounded = round(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    t.true(almostEqual(allInUSD(rounded.result, pricing), value));
+    t.true(almostEqual(allInUSD(bnb.result, pricing), value));
+    t.true(almostEqual(allInUSD(enumerated.result, pricing), value));
+
+    t.true(rounded.diff >= enumerated.diff);
+    t.true(bnb.diff >= enumerated.diff);
+});
+
+test("Target to exactly x + half a stock must be rounded up for optimal result", t => {
+    const value = 1000;
+    const pricing = {
+        AAPL: 2,
+        GOOG: 499,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.511,
+        GOOG: 0.489,
+        USD: 0,
+    };
+    const rounded = round(targets, value, pricing);
+    const bnb = branchAndBound(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    t.true(rounded.result.USD >= 0);
+    t.true(rounded.diff <= enumerated.diff);
+    t.true(bnb.result.USD >= 0);
+    t.true(bnb.diff <= enumerated.diff);
+});
+
+//This test requires an optimal solved solution first
+test.skip("Rounding up can not have negative consequences on portfolio closeness -- >0.5 + lower price rounded up", t => {
+    const value = 1000;
+    const pricing = {
+        AAPL: 2,
+        GOOG: 489,
+        USD: 1,
+    };
+    const targets = {
+        AAPL: 0.511,
+        GOOG: 0.489,
+        USD: 0,
+    };
+    const rounded = round(targets, value, pricing);
+    const enumerated = enumeration(targets, value, pricing);
+    const resultbnb = branchAndBound(targets, value, pricing);
+    t.true(resultRound.result.USD >= 0);
+    t.true(resultRound.diff <= resultEnum.diff);
+});
+
+test("Left over cash is computed correctly", t => {
+    const pricing = {
+        AAPL: 100,
+        GOOG: 200,
+        USD: 1,
+    };
+    const positions = {
+        AAPL: 20,
+        GOOG: 10,
+        USD: 0,
+    };
+
+    t.is(leftOverCash(positions, 4000, pricing), 0);
+    t.is(leftOverCash(positions, 4800, pricing), 800);
+    t.is(leftOverCash({ ...positions, USD: 300 }, 4800, pricing), 800);
+});

src/stores/account.js

@@ -0,0 +1,12 @@
+const memoryBackend = require("./backend/account/memory.js");
+//Data-related logic would live here. For example caching.  Since we only
+//have a in-memory implementation for now, caching is useless.
+//This is also where the data API is defined, abstracting the underlying storage
+//system.
+
+module.exports = function ({
+    accounts = undefined,
+    backend = memoryBackend({ accounts }),
+} = {}) {
+    return backend;
+};

src/stores/backend/account/memory.js

@@ -0,0 +1,89 @@
+//This module exists only for simplicity allowing the application to be run without hosting a database.
+const uuidv4 = require("uuid/v4");
+
+//Default accounts as provided in the requirements
+const _id = 1;
+const _accounts = {
+    [_id]: {
+        id: _id,
+        openPositions: {
+            AAPL: 50,
+            GOOG: 200,
+            CYBR: 150,
+            ABB: 900,
+            USD: 0,
+        },
+        targets: {
+            AAPL: 0.22,
+            GOOG: 0.38,
+            GFN: 0.25,
+            ACAD: 0.15,
+            USD: 0,
+        },
+    },
+};
+
+module.exports = function ({ accounts = _accounts } = {}) {
+    //Use JSON instead of adding Lodash for cloneDeep.
+    //This isn't a real use-case anyways since this would be a database implementation.
+    accounts = JSON.parse(JSON.stringify(accounts));
+    const addTargets = (id, targets, destination) => {
+        Object.keys(targets).forEach(
+            k => (destination[k] = [...(destination[k] || []), id]),
+        );
+    };
+    const addOpenPositions = (id, positions, destination) => {
+        Object.keys(positions).forEach(
+            k => (destination[k] = [...(destination[k] || []), id]),
+        );
+    };
+    const {
+        accountIdsByOpenPositions,
+        accountIdsByTargetPositions,
+    } = Object.entries(accounts).reduce(
+        (acc, [id, { openPositions, targets }]) => {
+            addTargets(id, targets, acc.accountIdsByTargetPositions);
+            addOpenPositions(id, openPositions, acc.accountIdsByOpenPositions);
+            return acc;
+        },
+        { accountIdsByOpenPositions: {}, accountIdsByTargetPositions: {} },
+    );
+
+    const addAccount = (targets, accountId) => {
+        const id = accountId || uuidv4();
+        accounts[id] = { id, openPositions: {}, targets: { ...targets } };
+        addTargets(id, targets, accountIdsByTargetPositions);
+        return id;
+    };
+
+    const setOpenPositions = (accountId, positions) => {
+        const account = accounts[accountId];
+        if (account) {
+            account.openPositions = positions;
+            addOpenPositions(accountId, positions, accountIdsByOpenPositions);
+        } else {
+            throw new Error("Can't set positions to a non-existing account");
+        }
+    };
+    const get = uuid => ({ ...accounts[uuid] });
+    const getAccountsByOpenPosition = ticker => [
+        ...(accountIdsByOpenPositions[ticker] || []),
+    ];
+    const getAccountsByTargetPosition = ticker => [
+        ...(accountIdsByTargetPositions[ticker] || []),
+    ];
+    const getAccountsByPosition = ticker =>
+        new Set([
+            ...getAccountsByOpenPosition(ticker),
+            ...getAccountsByTargetPosition(ticker),
+        ]);
+
+    return {
+        addAccount,
+        get,
+        getAccountsByOpenPosition,
+        getAccountsByTargetPosition,
+        getAccountsByPosition,
+        setOpenPositions,
+    };
+};

src/stores/backend/account/memory.spec.js

@@ -0,0 +1,72 @@
+const test = require("ava");
+const uuidv4 = require("uuid/v4");
+const accountBackend = require("./memory");
+
+test.beforeEach(t => {
+    const accountId = uuidv4();
+    const accounts = {
+        [accountId]: {
+            openPositions: {
+                AAPL: 50,
+                GOOG: 200,
+                CYBR: 150,
+                ABB: 900,
+                USD: 0,
+            },
+            targets: {
+                AAPL: 0.22,
+                GOOG: 0.38,
+                GFN: 0.25,
+                ACAD: 0.15,
+                USD: 0,
+            },
+        },
+    };
+    t.context.backend = accountBackend({ accounts });
+    t.context.accountId = accountId;
+    t.context.accounts = accounts;
+});
+
+test("Accounts can be retrieved by ID, a copy is returned", t => {
+    const { backend, accountId, accounts } = t.context;
+    const fromBackend = backend.get(accountId);
+    const original = accounts[accountId];
+    t.deepEqual(fromBackend, original);
+    t.not(fromBackend, original);
+});
+
+test("Accounts can be retrieved by ticker", t => {
+    const { backend, accountId, accounts } = t.context;
+    t.deepEqual(Array.from(backend.getAccountsByPosition("ABB")), [accountId]);
+    t.deepEqual(Array.from(backend.getAccountsByOpenPosition("ABB")), [
+        accountId,
+    ]);
+    t.deepEqual(Array.from(backend.getAccountsByTargetPosition("ACAD")), [
+        accountId,
+    ]);
+});
+
+test("If no accounts have the requested position, an empty array is returned", t => {
+    const { backend, accountId, accounts } = t.context;
+    t.deepEqual(Array.from(backend.getAccountsByPosition("AAA")), []);
+    t.deepEqual(Array.from(backend.getAccountsByOpenPosition("AAA")), []);
+    t.deepEqual(Array.from(backend.getAccountsByTargetPosition("AAA")), []);
+});
+
+test("An account can be added and retrieved by target position or id", t => {
+    const { backend, accountId, accounts } = t.context;
+    const targets = {
+        "QBTC.u": 0.66,
+        VOO: 0.33,
+        USD: 0,
+    };
+    const newAccountId = backend.addAccount(targets);
+
+    const newAccount = {
+        id: newAccountId,
+        targets,
+        openPositions: {},
+    };
+    t.deepEqual(backend.get(newAccountId), newAccount);
+    t.deepEqual(backend.getAccountsByTargetPosition("QBTC.u"), [newAccountId]);
+});

src/stores/backend/pricing/memory.js

@@ -0,0 +1,9 @@
+module.exports = (cache = {}) => ({
+    get: ticker => Math.max(+cache[ticker], 0) || undefined,
+    set: (ticker, price) => (cache[ticker] = Math.max(0, +price) || undefined),
+    subset: (...tickers) =>
+        tickers.reduce((acc, ticker) => {
+            acc[ticker] = cache[ticker];
+            return acc;
+        }, {}),
+});

src/stores/backend/pricing/memory.spec.js

@@ -0,0 +1,57 @@
+const test = require("ava");
+const memoryBackend = require("./memory.js");
+
+test("Pricing for a ticker can be fetched", t => {
+    t.is(memoryBackend({ AAPL: 100 }).get("AAPL"), 100);
+});
+
+test("Pricing for a ticker can be set", t => {
+    const pricing = memoryBackend({ AAPL: 100 });
+    pricing.set("AAPL", 101);
+    t.is(pricing.get("AAPL"), 101);
+});
+
+test("Pricing for a ticker can be removed", t => {
+    const pricing = memoryBackend({
+        AAPL: 100,
+        GOOG: 1000,
+        AMZN: 2000,
+        TSLA: 3000,
+    });
+
+    pricing.set("AAPL", 0);
+    pricing.set("GOOG", null);
+    pricing.set("AMZN", false);
+    pricing.set("TSLA", -1);
+
+    t.is(pricing.get("AAPL"), undefined);
+    t.is(pricing.get("GOOG"), undefined);
+    t.is(pricing.get("AMZN"), undefined);
+    t.is(pricing.get("TSLA"), undefined);
+});
+
+test("Missing pricing gives undefined", t => {
+    const pricing = memoryBackend({
+        AAPL: 0,
+        GOOG: null,
+        AMZN: undefined,
+        TSLA: -1,
+    });
+
+    t.is(pricing.get("AAPL"), undefined);
+    t.is(pricing.get("GOOG"), undefined);
+    t.is(pricing.get("AMZN"), undefined);
+    t.is(pricing.get("TSLA"), undefined);
+    t.is(pricing.get("NONE"), undefined);
+});
+
+test("A subset of ticker values can be obtained", t => {
+    const pricing = memoryBackend({
+        AAPL: 100,
+        GOOG: 1000,
+        AMZN: 2000,
+        TSLA: 3000,
+    });
+
+    t.deepEqual(pricing.subset("AAPL", "AMZN"), { AAPL: 100, AMZN: 2000 });
+});

src/stores/pricing.js

@@ -0,0 +1,20 @@
+const memoryBackend = require("./backend/pricing/memory.js");
+
+const globalCache = {};
+let globalInstance;
+
+function global({ seed = {}, backend = memoryBackend } = {}) {
+    if (!globalInstance) {
+        Object.assign(globalCache, seed, { USD: 1 });
+        globalInstance = backend(globalCache);
+    }
+    return globalInstance;
+}
+
+function instance({ cache = {}, backend = memoryBackend } = {}) {
+    return backend(Object.assign(cache, { USD: 1 }));
+}
+module.exports = {
+    global,
+    instance,
+};

test

@@ -0,0 +1,13 @@
+AAPL
+GOOG
+GFN
+ACAD
+CYBR
+ABB
+
+AAPL:1000
+rebalance:1
+GOOG:1
+rebalance:1
+
+