How do stock buybacks work, and how do index funds handle them?

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Tamalak
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How do stock buybacks work, and how do index funds handle them?

Post by Tamalak » Mon May 14, 2018 3:39 pm

Say there are only two corporations in the world, A and B. Each have a market cap of 1 billion. Vanguard's total stock fund owns 10% of each, 100 million. Vanguard's goal is to continue to own an equal percentage of each company, since correct indexing is done by capitalization.

Corporation A puts out a $500 million dividend, cutting its market cap in half. CorpA now has a cap of $500m, Vanguard owns $50m of it, CorpB still has a cap of $1bil, Vanguard owns $100m. Vanguard still owns the same % of each company (10%), so no adjustments are necessary. Vanguard distributes the dividend to its fund owners who decide for themselves how to use it.

Corporation B, instead of a dividend, does a stock buyback of half their shares. Since the buybacks are done on the active market, none of the shares Vanguard owns are bought back. This action reduces Corp B's market cap to $500m, but each share is now worth double the percentage of the company that it was. Since the market cap halved but the per-share value doubled, Vanguard still owns $100m of CorpB - 20%, but only 10% of CorpA. Vanguard is no longer investing proportional to capitalization. What's the accepted methodology to fix this?

mak1277
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Re: How do stock buybacks work, and how do index funds handle them?

Post by mak1277 » Mon May 14, 2018 3:44 pm

Tamalak wrote:
Mon May 14, 2018 3:39 pm

Corporation B, instead of a dividend, does a stock buyback of half their shares. Since the buybacks are done on the active market, none of the shares Vanguard owns are bought back. This action reduces Corp B's market cap to $500m, but each share is now worth double the percentage of the company that it was. Since the market cap halved but the per-share value doubled, Vanguard still owns $100m of CorpB - 20%, but only 10% of CorpA. Vanguard is no longer investing proportional to capitalization. What's the accepted methodology to fix this?
Share buybacks don't automatically reduce market cap.

If the # of outstanding shares was halved, but the stock price doubled as in your example, market cap wouldn't be changed at all.

1,000 shares x $10/share = market cap of $10,000
500 shares x $20/share = market cap of $10,000

Tamalak
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Re: How do stock buybacks work, and how do index funds handle them?

Post by Tamalak » Mon May 14, 2018 3:48 pm

mak1277 wrote:
Mon May 14, 2018 3:44 pm
Tamalak wrote:
Mon May 14, 2018 3:39 pm

Corporation B, instead of a dividend, does a stock buyback of half their shares. Since the buybacks are done on the active market, none of the shares Vanguard owns are bought back. This action reduces Corp B's market cap to $500m, but each share is now worth double the percentage of the company that it was. Since the market cap halved but the per-share value doubled, Vanguard still owns $100m of CorpB - 20%, but only 10% of CorpA. Vanguard is no longer investing proportional to capitalization. What's the accepted methodology to fix this?
Share buybacks don't automatically reduce market cap.

If the # of outstanding shares was halved, but the stock price doubled as in your example, market cap wouldn't be changed at all.

1,000 shares x $10/share = market cap of $10,000
500 shares x $20/share = market cap of $10,000
Is this realistic for buybacks? That means if I have shares of a company that buys back, my net worth reliably increases. Versus with dividends, net worth typically doesn't change.

It seems to me that the market cap of a company that buys back should go down, because the company just spent a lot of money on things that it immediately annuls. The company's balance sheet is worse than it was.

And regardless of what happens to the market cap, Vanguard now owns a greater % of that company than it did before, whereas the goal for index-by-capitalization is to own an equal % of each company.

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Mon May 14, 2018 3:51 pm

mak1277 wrote:
Mon May 14, 2018 3:44 pm
Share buybacks don't automatically reduce market cap.
First, share buy backs affect market cap in exactly the same way as dividends. In theory the market cap should drop by the amount of cash returned to the shareholders.

Second, distributed cash - like dividends - are reinvested back into the index at the market weight on the day received.

Third, stock buy backs are handled exactly the same as dividends. Dividends have clean data - you know ahead of time exactly the amount and the date and the impact on market cap. Buybacks have dirty data. You know after the fact exactly the amount and about what dates and about what impact it had. You sell shares to match the buyback and reinvest the money back into the index.

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Mon May 14, 2018 3:54 pm

Tamalak wrote:
Mon May 14, 2018 3:48 pm
Is this realistic for buybacks? That means if I have shares of a company that buys back, my net worth reliably increases. Versus with dividends, net worth typically doesn't change.

It seems to me that the market cap of a company that buys back should go down, because the company just spent a lot of money on things that it immediately annuls. The company's balance sheet is worse than it was.
With dividends, the stock falls by the amount of dividends. With a buyback your share price does not change.

In either case the market cap falls by the amount distributed.

At least in the short run. Long run depends on Free Cash Flow to Equity and the quality of that FCFE.

mak1277
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Re: How do stock buybacks work, and how do index funds handle them?

Post by mak1277 » Mon May 14, 2018 3:57 pm

alex_686 wrote:
Mon May 14, 2018 3:51 pm
mak1277 wrote:
Mon May 14, 2018 3:44 pm
Share buybacks don't automatically reduce market cap.
First, share buy backs affect market cap in exactly the same way as dividends. In theory the market cap should drop by the amount of cash returned to the shareholders.
But this isn't the way it works in practice. First, the company is buying back shares on the open market...share buying generally (by anyone) leads to a higher share price. Second, buying back shares means that the same amount of earnings is allocated to a smaller number of shares (EPS goes up). If the P/E multiple stays the same, the stock price rises. How many people are trading off of book value of assets vs. future earnings?

jalbert
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Re: How do stock buybacks work, and how do index funds handle them?

Post by jalbert » Mon May 14, 2018 4:05 pm

A float-adjusted stock index fund would track the index. Rebalancing is not needed if only capitalization of holdings change, but if the index provider adjusts the free float of a stock, whether due to buybacks or just “private” shares being added to or removed from the tradable universe, then a fund that tracks the index would have to rebalance to track the new free float weights.
Risk is not a guarantor of return.

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Mon May 14, 2018 4:07 pm

mak1277 wrote:
Mon May 14, 2018 3:57 pm
But this isn't the way it works in practice. First, the company is buying back shares on the open market...share buying generally (by anyone) leads to a higher share price. Second, buying back shares means that the same amount of earnings is allocated to a smaller number of shares (EPS goes up). If the P/E multiple stays the same, the stock price rises. How many people are trading off of book value of assets vs. future earnings?
Read up on Modigliani and Miller Capital Structure Theory. Written in the 1950s, won a Nobel, bedrock of investment theory.

Why would a company buying shares rise the price? There are lots of other people buying shares along with the company. Just another small fish. Empirical evidence is thin.

Yes, buy backs do increase the earnings per share, which is a good thing. It also increases leverage, which increases risk, which is a bad thing.

The trick is that the "Enterprise Value" of a company stays the same no matter how you structure it. Pay out dividends. Borrow money to do a share buy back. etc. The economic value of the company remains constant no matter how the CFO dresses up the company. If this was not true then the CFO could make money from nothing.

Now there are preferred states of dress. Investors like some but not a lot of leverage. The is a optimal balance to satisfy investor's risk level.

Tamalak
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Re: How do stock buybacks work, and how do index funds handle them?

Post by Tamalak » Mon May 14, 2018 4:20 pm

jalbert wrote:
Mon May 14, 2018 4:05 pm
A float-adjusted stock index fund would track the index. Rebalancing is not needed if only capitalization of holdings change, but if the index provider adjusts the free float of a stock, whether due to buybacks or just “private” shares being added to or removed from the tradable universe, then a fund that tracks the index would have to rebalance to track the new free float weights.
Does this mean that if I hold a world cap index, the % of the world cap I own would slowly increase? Since buybacks would first increase the % of THAT company I own, and then the fund would rebalance which increases the % of the world that I own.
Last edited by Tamalak on Mon May 14, 2018 4:25 pm, edited 2 times in total.

CantPassAgain
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Re: How do stock buybacks work, and how do index funds handle them?

Post by CantPassAgain » Mon May 14, 2018 4:20 pm

mak1277 wrote:
Mon May 14, 2018 3:57 pm
But this isn't the way it works in practice. First, the company is buying back shares on the open market...
Not necessarily

jalbert
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Re: How do stock buybacks work, and how do index funds handle them?

Post by jalbert » Tue May 15, 2018 11:09 pm

Does this mean that if I hold a world cap index, the % of the world cap I own would slowly increase?

Since buybacks would first increase the % of THAT company I own, and then the fund would rebalance which increases the % of the world that I own.
I'm not clear what you are asking. If a company does a buyback, it will have fewer free-float shares, but each share will be more valuable. If this results in an overall decrease (or increase) in free-float market cap, then the weighting of the stock in any free-float market cap index containing the stock with decrease (or increase) commensurate with the change in free-float market cap, all else being equal.

Of course all else is not equal. Market caps of stocks change every day, and free-floats change from time to time. I think daily market movements of stocks have the biggest impact on index weightings. A fund only needs to rebalance if a stock's free float market cap percentage in the index changes.
Risk is not a guarantor of return.

rob65
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Re: How do stock buybacks work, and how do index funds handle them?

Post by rob65 » Wed May 16, 2018 2:46 am

If an index fund has assets equal to p% of the total market cap of the index, it will own p% of the available shares of each stock in the index.

Consider an index with three companies X, Y, and Z.

Company X: 1000 shares, $10 per share, market cap = $10,000
Company Y: 500 shares, $12 per share, market cap = $6000
Company Z: 2000 shares, $2 per share, market cap = $4000

Total Market Cap = $20,000

Our index will be 50% Company X, 30% Company Y, and 20% Company Z.

Suppose our fund has assets of $2000, so 10% of the total market cap.

Our fund would then have $1000 in Company X, $600 in Company Y, and $400 in Company Z.

That translates to 100 shares of Company X, 50 shares of Company Y, and 200 shares of Company Z.

We own 10% of the shares of Company X, 10% of the shares of Company Y, and 10% of the shares of Company Z.

For fun with algebra, suppose there are x shares of Company X at p dollars per share, y shares of Company Y at q dollars per share, z shares of Company Z at r dollars per share. I'll use standard algebra notation with juxtaposition denoting multiplication. The total market cap is xp+yq+zr; let's denote that total by M. The proportion of the index made up by Company X is (xp)/M. Suppose our fund has total assets of T dollars. Our fund should have Txp/M dollars in Company X. At p dollars per share, that means we should own Tx/M shares in company X. There are x shares in company A, so the proportion of the shares of Company X that we own is T/M. Repeat to see that the proportion of Company Y shares that we own is also T/M. The same with company Z.

Notice that a change in share price doesn't change anything. Suppose stock X changes to s dollars per share. Let N = xs+yq+zr be the new total market cap. We own Tx/M shares in X, Ty/M shares in Y, and Tz/M shares in Z. Our fund is now worth U = sTx/M+qTy/M+rTz/M = (Txs+Tqy+Trz)/M = T(xs+qy+rz)/M = TN/M. It follows that U/N = T/M. In other words, we still own the same percentage of the total market and the same percentage of each company.

However, if the number of shares changes, then that does create something that the fund has to deal with. We just saw that we must own an equal percentage of the available shares of each stock in the index. If a company buys back stock (and our shares aren't proportionally bought back in the buyback), then we will be over-weighted in that stock.

Now, I'm not an expert. There may be complications that I'm ignoring. This is certainly an idealized market. In real life, you would have to deal with free-float. Also, the fund would have constant inflows and outflows, so it's market share would be constantly changing. There could be liquidity issues with some stocks. However, I don't think any of that fundamentally changes the basic conclusions. Again, it's certainly possible that I'm overlooking something that complicates this in real life.

Edit: My guess is that big funds can handle changes in free-float with their inflows and outflows; Vanguard also has a patented process that allows them to use the etf creation/redemption process to avoid creating capital gains. (How that works is way above my head.)

Valuethinker
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Re: How do stock buybacks work, and how do index funds handle them?

Post by Valuethinker » Wed May 16, 2018 3:54 am

alex_686 wrote:
Mon May 14, 2018 4:07 pm
mak1277 wrote:
Mon May 14, 2018 3:57 pm
But this isn't the way it works in practice. First, the company is buying back shares on the open market...share buying generally (by anyone) leads to a higher share price. Second, buying back shares means that the same amount of earnings is allocated to a smaller number of shares (EPS goes up). If the P/E multiple stays the same, the stock price rises. How many people are trading off of book value of assets vs. future earnings?
Read up on Modigliani and Miller Capital Structure Theory. Written in the 1950s, won a Nobel, bedrock of investment theory.

Why would a company buying shares rise the price? There are lots of other people buying shares along with the company. Just another small fish. Empirical evidence is thin.

Yes, buy backs do increase the earnings per share, which is a good thing. It also increases leverage, which increases risk, which is a bad thing.

The trick is that the "Enterprise Value" of a company stays the same no matter how you structure it. Pay out dividends. Borrow money to do a share buy back. etc. The economic value of the company remains constant no matter how the CFO dresses up the company. If this was not true then the CFO could make money from nothing.
If interest is tax deductible business expense that is not true? You can create value for equity holders by increasing leverage?

I am ignoring agency costs here, that's a separate argument.
Now there are preferred states of dress. Investors like some but not a lot of leverage. The is a optimal balance to satisfy investor's risk level.
With no taxes and no other costs (agency, liquidity, bankruptcy)?

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Wed May 16, 2018 9:04 am

Valuethinker wrote:
Wed May 16, 2018 3:54 am
If interest is tax deductible business expense that is not true? You can create value for equity holders by increasing leverage?

I am ignoring agency costs here, that's a separate argument.
Now there are preferred states of dress. Investors like some but not a lot of leverage. The is a optimal balance to satisfy investor's risk level.
With no taxes and no other costs (agency, liquidity, bankruptcy)?
Points.

M&M assumes no tax shield for bonds, companies don't go bankrupt, and a few others assumptions. In a idealized world a investor does not care if the company is funded by 1% debt / 99 equity or 99% / 1% equity. It gets more interesting and complex as you relax the assumptions. Empirically M&M holds up strongly.

We can now look at second order impacts. You bring up the tax shield and agency issues, which are good points.

But I am going to clarify my point on leverage. Leverage and debt loads have expanded and contracted over the years. In the 1950s investors craved low risk and steady dividends. In the 1980s investors preferred high risk, high returns, and increasing dividends. Today we have backed off somewhat on the risk. We are o.k. with lumpy stock buy backs replacing steadily increasing dividends. Who knows what tomorrow will bring. Taxes, agency issues, etc. do have a impact of investor's preferred leverage.

jalbert
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Re: How do stock buybacks work, and how do index funds handle them?

Post by jalbert » Wed May 16, 2018 10:19 pm

However, if the number of shares changes, then that does create something that the fund has to deal with. We just saw that we must own an equal percentage of the available shares of each stock in the index. If a company buys back stock (and our shares aren't proportionally bought back in the buyback), then we will be over-weighted in that stock.
For a float-adjusted Index, the fund should only have to rebalance if the free float market cap weight changes, which depends on whether a price movement from the buyback offsets the reduction in free float shares.
Risk is not a guarantor of return.

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Thu May 17, 2018 10:20 am

jalbert wrote:
Wed May 16, 2018 10:19 pm
For a float-adjusted Index, the fund should only have to rebalance if the free float market cap weight changes, which depends on whether a price movement from the buyback offsets the reduction in free float shares.
You don't have to adjust float-adjusted indexes when a stock changes price, you change when the capital structure changes.

For example, lets us say that Vanguard owns 5% of the market. That is 5% of each company. When the stock price change Vanguard's owners does not change so it has to do nothing. On the other hand if the company changes it capital structure by either issuing new shares or removing shares from the market - like in a stock buy back - Vanguard needs to buy and sell to reflect the new reality.

jalbert
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Re: How do stock buybacks work, and how do index funds handle them?

Post by jalbert » Thu May 17, 2018 4:14 pm

alex_686 wrote:
Thu May 17, 2018 10:20 am
jalbert wrote:
Wed May 16, 2018 10:19 pm
For a float-adjusted Index, the fund should only have to rebalance if the free float market cap weight changes, which depends on whether a price movement from the buyback offsets the reduction in free float shares.
You don't have to adjust float-adjusted indexes when a stock changes price, you change when the capital structure changes.
Correct. You have to rebalance if free float weights change. My point was that a shard buyback reduces the number of fees float shares. Whether or not that leads to a change in free float cap weight depends on how the price changes in response to the buyback. As long as price movements offset the reduction in shares so that free float market cap weight in the index doesn’t change I don’t think a rebalance would be needed.
Risk is not a guarantor of return.

alex_686
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Re: How do stock buybacks work, and how do index funds handle them?

Post by alex_686 » Thu May 17, 2018 4:41 pm

jalbert wrote:
Thu May 17, 2018 4:14 pm
Correct. You have to rebalance if free float weights change. My point was that a shard buyback reduces the number of fees float shares. Whether or not that leads to a change in free float cap weight depends on how the price changes in response to the buyback. As long as price movements offset the reduction in shares so that free float market cap weight in the index doesn’t change I don’t think a rebalance would be needed.
My point was that buy-backs always requires a rebalance, price movements never. Dig into the S&P or CSRP methodology whitepapers.

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