Solvency vs. Liquidity: Not the Same Beast
Let’s clear the fog: Solvency means you own more than you owe—you’re still king $($or queen$)$ of your balance sheet. Liquidity, on the other hand, is whether you can pay your bills on time—kingdom or not.
So if solvency is about wealth, liquidity is about cash in hand.
In trading, liquidity means how quickly and cheaply you can sell something. Highly liquid? Large-cap stocks. Illiquid? That dusty old startup bond nobody wants anymore.
What Affects the Price When You Sell?
Your selling price depends on:
- The asset’s fair value $($a.k.a. mid-market price$)$.
- How fast you need to sell $($desperation discount alert$)$.
- How much you’re selling $($big orders = big problems$)$.
- Overall market conditions $($panic sells everything$)$.
Think of it like selling pizza. One slice? Easy. A whole truckload at 2 a.m.? Good luck.
Predatory Traders: Sharks in the Liquidity Pool 🦈
Large trades create a scent in the market. Other traders sniff out your desperation and start moving ahead of you. That’s predatory trading.
Imagine you’re trying to cover a short by buying shares. If others know, they’ll buy first, push up the price, and sell back to you at a profit.
Market = jungle. Predators win.
Transparency Matters: The 2008 Ghost Asset Fiasco
In the 2000s, people bought mortgage-backed portfolios they didn’t understand. No models. No visibility. So when the 2007–08 crisis hit, no one could price them.
Result? Those assets became financial black holes. No price = no buyer = no liquidity.
Bid-Offer Spread: Your Hidden Trading Tax
Market makers quote:
- Bid price: what they’ll pay you.
- Offer price: what you must pay them.
The bid-offer spread is the toll you pay just to play. It widens for big trades or thinly traded assets.
Definitions:
$p= \text{offer price} – \text{bid price}$
$s= \frac{\text{offer price} – \text{bid price}}{\text{mid-market price}}$
So, the bigger the spread, the bigger your cost.
💸 Cost of Liquidation in Normal Markets
Let:
- $s_i$ = proportional spread for asset $i$
- $\alpha_i$ = mid-market value of position $i$
- $n$ = number of positions
Then: $\text{Cost of Liquidation (Normal)} = \sum_{i=1}^{n} \frac{s_i \cdot \alpha_i}{2}$
Analogy:
This is like tipping your waiter 10
🧪 Example: Two Stocks, One Bill
ABC Company
- Shares = 2,000,000
- Bid = \$25.50, Offer = \$27.00
- Mid = \$26.25 → Value = \$52.5M
- Spread = \$1.50 → \$s = 0.05714$
XYZ Company
- Shares = 500,000
- Bid = \$45.00, Offer = \$46.50
- Mid = \$45.75 → Value = \$22.875M
- Spread = \$1.50 → \$s = \$0.03279
Cost of Liquidation: $\frac{52.5M \cdot 0.05714}{2} + \frac{22.875M \cdot 0.03279}{2} = \$1,874,9612$
But what if the market is panicking?
🧨 Cost of Liquidation in Stressed Markets
Now include:
- $\mu_i$ = mean spread
- $\sigma_i$ = standard deviation of spread
- $\gamma$ = confidence level (z-score)
Then: $\text{Cost of Liquidation (Stressed)} = \sum_{i=1}^{n} \frac{(\mu_i + \gamma \cdot \sigma_i) \cdot \alpha_i}{2}$
Example $($same stocks, now with panic$)$:
- $z = 1.645$ $($for 95% confidence$)$
- $\mu$ = $1.50$, $\sigma$ = $2.50$
ABC: $\mu_s = 0.05714$, $\sigma_s = 0.09524$
XYZ: $\mu_s = 0.03279$, $\sigma_s = 0.05464$
$\text{Cost} = \left( \frac{52.5M \cdot (0.05714 + 1.645 \cdot 0.09524)}{2} \right) + \left( \frac{22.875M \cdot (0.03279 + 1.645 \cdot 0.05464)}{2} \right) = \$7,015,577$
Lesson? Stress costs $$$.
🔥 Liquidity-Adjusted VaR $($LVaR$)$
Standard VaR ignores liquidity. LVaR says: “What if we also count the cost of exiting?”
In normal market:
$\text{LVaR (normal)} = \text{VaR} + \sum_{i=1}^{n} \frac{s_i \cdot \alpha_i}{2}$
In stressed market:
$\text{LVaR (stressed)} = \text{VaR} + \sum_{i=1}^{n} \frac{(\mu_i + \gamma \cdot \sigma_i) \cdot \alpha_i}{2}$
This is your VaR with an exit strategy. Because being right doesn’t matter if you can’t sell.
⏱️ The Trader’s Dilemma: Fast or Slow?
- Fast Unwind = avoids price risk, but spreads widen.
- Slow Unwind = tighter spreads, but market risk grows.
The trader’s goal? Minimize total VaR.
Total Cost of Bid-Offer Spread: $\sum_{i=1}^{n} \frac{p(q_i)}{2}$
Variance of Position: $\sum_{i=1}^{n} \sigma^2 x_i^2$
Trader’s Objective: $\text{Minimize: } \sqrt{ \sum_{i=1}^{n} \sigma^2 x_i^2 } + \sum_{i=1}^{n} \frac{p(q_i)}{2}$
Where:
- $n$ = days to unwind
- $q_i$ = units traded on day $i$
- $x_i$ = size of position on day $i$
📊 A Final Word: Amihud’s Illiquidity Measure
Economist Yakov Amihud gave us: $\text{Illiquidity} = \frac{|\text{daily return}|}{\text{dollar volume}}$
Higher number = lower liquidity. Translation: When volume is low and prices are jumpy, your asset is dangerous to exit.
Amihud also found: lower liquidity = higher expected returns. Why? Investors want extra compensation for the exit headache.
🚪 The Bigger Picture: Always Know the Exit
- Illiquidity can turn a good trade into a nightmare.
- Bid-offer spreads are your silent enemy.
- LVaR = VaR + exit cost $($a realistic risk measure$)$.
- Always plan your exits—before entering.