*September 16, 2020*

One question I’ve gotten from readers a few times over the years is whether the participation in a so-called Employee Stock Purchase Plan (ESPP) is worthwhile.

A little bit of background: some corporations offer their employees to buy stocks of their company at a discount of up to 15%. There are some strings attached, though. For example, there are often minimum holding periods, anywhere between a few months and up to two years. The discount is also taxed as ordinary income, though the subsequent capital gains may qualify for treatment as long-term gains.

**If** you can liquidate the stocks right away and pocket the discount, then participating is likely a no-brainer. Take the money out of the ESPP and invest it in a low-cost index fund. It’s a nice boost to your contributions in your taxable account after you’ve maxed out all your other tax-advantaged options. 15% adjusted by your marginal income tax rate – federal and state. That would still be more than 10% for most people! Pretty sweet!

But what should you do if there’s a minimum holding period? During that time, part of your portfolio is now concentrated in one single corporation. The opposite of diversification. So, it’s a tradeoff: You get the discount but you also take on additional risk. Is it still worthwhile? This is an inherently **quantitative** question. Without putting hard numbers behind this we can talk about this until the cows come home. The only way to answer this question is through a quantitative exercise. And it turns out, the numbers look like it’s indeed worthwhile to participate in an ESPP, especially if you can get the full 15% discount, the maximum allowed under federal law.

Let’s take a closer look…

### Tax treatment

Before we even get started with any computations, let’s first look at the tax issues associated with ESPPs. I’m not a tax guru, so I have to rely on some other experts on this one:

- Turbotax: Employee Stock Purchase Plans
- The Motley Fool: How to Get the Most From Your Employee Stock Purchase Plan

**The ESPP Discount:** What I gathered from the experts is that the discount your company offers you is always taxed as **ordinary** income. That’s consistent with my own past experience when I was still working and participated in the ESPP; the discount always showed up as ordinary income on the W-2 the same year I received the discount (not when I sold the stock). But I’ve also heard from others who found that the discount doesn’t show up on their tax documents until they actually sell the shares.

**Dividends along the way:** I got annual 1099-DIV statements. So, dividends were treated just like in any other equity investment. If you work for a non-REIT U.S. corporation and you satisfy all the minimum holding period requirements (*“more than 60 days during the 121-day period starting 60 days prior to the ex-dividend date for common stocks”*) then your dividends along the way should be qualified dividends and enjoy the lower rate on your federal return!

**Capital gains:** Gains will be considered “long-term” when you dispose of the shares at least 2 years after the “offer period” and at least 1 year after the exercise date. And “short-term” gains otherwise.

**Side note:** There’s a potential additional benefit in some ESPPs in that they would accumulate your contributions over a certain offer period window. But when you buy the shares at the end of that window you can do so at the lowest (daily closing) price observed during that window. That’s an additional discount on top of the 15%.

### Efficient Frontiers with an ESPP

Let’s first check whether we should allocate **any** share of the portfolio at all to the ESPP. I propose we look efficient frontiers (EF) with and without the ESPP and check if and how the addition of an ESPP moves the EF and improves our risk vs. return tradeoff.

To set up an efficient frontier analysis, we need only a handful of inputs: expected returns and risk and correlation measures. Let’s start with a baseline portfolio with only a broad stocks index (S&P 500) and intermediate U.S. Treasury bonds (i.e., 10-years to maturity):

- Equity risk 15%, return 6.0%. 15% is the approximate long-term annualized risk of the S&P 500 (monthly data, annualized) and I assume a 6% nominal annualized return (i.e., about 2% inflation + 4% real return). A little bit more conservative than the very long-term average real return (about 6.7%), but we want to be cautious in light of the expensive CAPE ratio these days.
- Bond risk/return: 6.0% risk (realized risk over the last 10+ years) and 0.7% return (=current 10-year bond yield).
- Stock/Bond correlation: -0.30, roughly in line with the monthly correlation over the last 10+ years.
- I also assume that the risk-free, short-term government bond rate is 0.10%. It’s not needed for the baseline, but I always include the risk-free rate in my EF diagrams.

How about the stock return inputs? I assume that the company stock has an equity beta of 1.0, a correlation with the stock index of 0.6, and a correlation with the bond portfolio of -0.15. All these inputs vary quite substantially among the individual stocks you might find in the S&P 500. But you have to start somewhere. I will do some robustness analysis and confirm that changing these stock parameters will not change the results all that much. Only the ESPP discount really matters here!

If we believe in the CAPM model then a stock with a beta of 1 will have the same expected return as the index (and it’s “RiskFree + beta*(StockIndex-RiskFree” for all other betas in general). Let’s assume that the stock with the ESPP will also get a return boost of 5% annualized. Think about this as a 10% (net, after-tax) discount spread over a mandatory minimum holding period of 2 years. We can look at some other parameterizations later.

Also, notice that the four “risk variables”: beta, stock/index correlation, index risk, and stock risk are tied together through the formula:

Beta=Correlation*StockRisk/IndexRisk,…

thanks to basic statistics/econometrics in univariate regression models. So, we can pick only 3 of the parameters and the fourth is determined through the statistical identity above. In this case, the stock risk has to be 25% to be consistent with the other three parameters. Sorry about the math excursion but this is important stuff if want to do an Efficient Frontier analysis.

So, I plug that all into my Matlab program and then run some Efficient frontier analysis. I compute three different efficient frontiers:

- The baseline with only the stock index and bond index fund
- Add the ESPP stock but restrict the weight of the ESPP to 10% of the portfolio. Think of this as someone who has a $200k and is allowed to invest up to $10k a year in the ESPP. Since you’ll have 2 rolling years of ESPP contributions, you can’t go much above 10% weight.
- Add the ESPP stock without any constraints. Say, you’re a young employee, straight out of college, just starting out with your first corporate job. You can probably have a much higher ESPP weight then.

Let’s take a look at the efficient frontiers first, see the chart below. Adding the ESPP will move the EF quite substantially to the left, which is the **desirable** area, i.e., less risk/more return. For example, instead of a 100% stock portfolio with a 6% return and 15% risk (the end-point of the baseline EF), you could generate an excess 1.3% return for the same level of risk. Or, for a given expected return level of 6%, you can reduce the risk by about 3 percentage points. That’s a major improvement in the risk/return tradeoff.

**Footnotes for the math geeks:**

*I chopped off the EFs at the point where they’d bend backward again toward the 100% bond allocation. That part is not normally considered part of the EF because you go into the “inefficient portion of lowering returns while increasing risk.**The efficient frontier is using the Matlab “quadprog” function. So you run a linear-quadratic optimization problem: minimize the variance w’∑w subject to the w’μ=target and the weight constraints (all weights between 0 and 1, all weights sum to 1 and, if applicable, addotional weight constraints, like ESPP below 10%).*

If you constrain the ESPP share to 10% you get less of a benefit. It means that the unconstrained EF wants to allocate significantly more than 10% of the portfolio to the ESPP. If you’re a young employee and you’ve maxed out all the tax-advantaged options, feel free to go crazy with the ESPP if you still have money left over!

Talking about allocations, we can also plot the portfolio weights as a function of the target expected return. Notice that the unconstrained frontier extends all the way to 11% expected return and 25% expected risk if you put 100% of your portfolio into the ESPP. The EF with the 10% constraint goes only up to about 6.5% expected return, so the allocation chart stops at that maximum expected return level when you hit the 10% ESPP, 90% equity index allocation.

There you have it! Despite the significantly higher risk in the individual stock (25% vs. the 15% index risk), the ESPP-advantaged investment should be in the portfolio along the efficient frontier.

Here’s another way to showcase the benefit you get from including the ESPP. Let’s start from a baseline of a 100% equity index investor (which was my own plan for much of my accumulation phase). With the inclusion of the ESPP, how much can we improve relative to the 100% equity index allocation with a 6% expected annual return and 15% risk? We can quantify that 2 different ways:

- Hold the expected return at 6%, by how much can I reduce the portfolio risk?
- Hold the risk target at 15%, by how much can I increase my expected return?

That’s what I do in the table below. And again, I display this for both the constrained ESPP (10% max) and the unconstrained weights:

- With a 6% return target, you can reduce the risk by about 1.4 and 3.0 percentage points, respectively. That’s about 10-20% less risk. Pretty good!
- With a 15% risk target, you can raise your expected returns by 0.46% and 1.28% p.a., respectively. That’s quite substantial!

### Robustness analysis

Let’s play around with some of the parameters here and see how they will impact the results. I will change one parameter at a time and leave the other parameters unchanged:

**1: Lower the ESPP alpha to 2% p.a.:**

If we lower the ESPP alpha to only 2% p.a., there’s still a role for participating in the plan. The unconstrained efficient frontier still wants to go to more than 10% into the ESPP. As expected, if you constrain the ESPP to no more than 10% of the portfolio you diminish the benefit relative to the 5% alpha case. But even at 2% alpha, this might still be worthwhile!

**2: Lower the ESPP alpha to 1% p.a.:**

With only 1% alpha p.a., we’re now getting pretty close to zero benefits. I’d probably pass on that opportunity.

**3: Increase the stock beta to 1.1**

I set the ESPP alpha back to 5% and now play around with the company stock market beta. The weighted index beta across all stocks in the index is 1.0, by definition. But it can vary quite a bit. Raising the beta 1.1 (thus, the stock moves, on average, 1.1% for every 1.0% the index moves) will not make a major difference in the results, see the table below. Especially the 10%-constrained portfolios are almost identical.

**4: Set company stock vs. bond correlation to 0:**

The overall index has a nice negative correlation with the bond market. If we set the correlation between your ESPP stock and the bond market to zero (less diversification with the bond market), will that invalidate the

Not really. The results are almost the same for the return/risk targets of 6%/15%. You had small bond allocation to begin with at that point, so playing around with the bond correlation should not change the results much.

**5: Lower the Stock vs. Index correlation to 0.5:**

Playing around with the company stock vs. index correlation is not going to change the results much either, see below:

### Caveats

As always, here are a few caveats to keep in mind:

**More correlations:** In the Efficient Frontier diagrams I only factor in the correlations **within** the financial asset portfolio. Keep in mind that your human capital, i.e., earnings potential is also highly correlated with your company stock, just ask the former employees of Enron. When I was still working in corporate America I had a not-so-generous ESPP, so I never participated all that much in the ESPP. Yeah, there was a small benefit from the plan but I decided to never plow much money into this because I didn’t want to compound my risk of working in one of the most volatile industries with very little job security! If the ESPP benefit gets too small you’d better pass on it!

**Transaction costs: ** Selling your shares in the ESPP might be significantly more expensive than the average commission you’ve become accustomed to in your discount online broker account. I’ve seen t-costs of $20 per transaction. It will likely not wipe out the entire benefit of the ESPP, but keep the t-costs in mind when planning the exit strategy. It might mean you’ll have to hold on to your ESPP lots a little bit longer to sell larger lots less frequently.

**Compounding taxes:** When you sell your ESPP shares to move the money to your preferred low-cost equity index fund, you have to pay for the capital gains. From a tax-minimization perspective, it’s always best to defer capital gains as long as possible. So going the ESPP route violates this principle and you might have a small tax drag from this.

### Conclusions

Especially an ESPP with a large enough discount will justify participation, despite the likely much higher risk in the individual stock. The results seem to be pretty robust even when playing around with the other stock parameters, like equity index beta, and correlations.

But the ESPP only makes sense until you reach the minimum holding period to reap the benefit of the discount! The individual stock **without** the return boost from the ESPP does not belong in your taxable portfolio! **Too much uncompensated risk!**

So it looks like the ESPP can be a good supplement to your taxable brokerage account. Instead of taking your net income and investing it in an (after-tax) index fund, first, funnel it through the ESPP and into the index fund after the minimum holding period. The 15% discount, probably 10% or more after taxes for most folks, is a nice boost for your retirement savings outside of your tax-advantaged accounts.

Talking about retirement accounts, one additional question I couldn’t tackle here today is whether the ESPP is actually so attractive that it beats your 401(k) contributions after maxing out the company match. That’s a topic for another post, hopefully, next week. So, stay tuned!

### Hope you enjoyed today’s post! Looking forward to your comments and suggestions below!

*Title Picture Credit: pixabay.com*

ERN: ” the discount always showed up as ordinary income on the W-2 the same year I received the discount (not when I sold the stock). ”

This has always been true for me, too. However, my new employer’s ESPP will report the discount as income in the year I SELL my shares, NOT the year I BOUGHT them. This was confusing at first, but that Turbotax article does seem to allow that. That can be very handy if I’m on the verge of retirement, since I can wait two years to sell the shares, when I might be in a lower tax bracket for the ordinary income from the discount. Not only that, if I can manage to get below $103K of income in the year I sell, then the long-term capital gains rate is ZERO (MFJ) for any extra growth on top of the discount!

Yes, although having an increased risk early on in your retirement probably isn’t ideal, unless you’re operating with a fairly conservative SWR.

The ESPP is likely a non-issue DURING retirement. If you have already 7-figure portfolio then the last 2 years of ESPP money is a drop in the bucket in overall portfolio.

IBM didn’t include the discount on W-2 either in purchase or sale year. It’s up the employee to report the discount as ordinary income in sales year. The discount is adjusted if sales price is less the fair market value on the grant date.

If you sell the shares “quickly”, the bargain element is reported on your W-2. If you wait “a while” before you sell, the bargain element is not reported on your W-2. I’m using vague terms and scare quotes because I don’t remember the exact times and when the clock starts ticking.

Gotcha. I guess every company manages this differently. It’s actually better if you self-report it in the year of selling it. Defers the tax burden.

Thanks for sharing. That is a nice feature because you delay the taxable income. Maybe you sell in the year when you leave work mid-year and your other ordinary income is low, pushing you into a lower bracket. Sweet!

>Let’s assume that the stock with the ESPP will also get a return boost of 5% annualized. Think about this as a 10% (net, after-tax) discount spread over a mandatory minimum holding period of 2 years.

I don’t think this does justice to the annualized returns of participating in an ESPP. In pre-tax terms, a 15% discount can translate into 88% annualized return (for the purchase period), not a 15% return. I will explain.

ESPP purchase periods are often 0.5 years, where you contribute money from each paycheck for 0.5 years, and then you purchase at a discount to the lower of the beginning or ending price. Your first contribution is tied up for 0.5 years and gives you roughly 1/(1-0.15)^2 = 1.38, a 38% annualized return. If your last contribution is the day before the purchase period, it’s annualized return is 1/(1-0.15)^365 = 6*10^25, an outrageous annualized return.

As an approximation, you can say your contribution money is tied up for an average of half of the 0.5 year purchase period, so the annualized return is roughly 1/(1-0.15)^4 = 1.92, a 92% annualized return. A more precise calculation results in 88% annualized return.

And you can get greater than a 15% discount on the stock at time of purchase if the stock went up during the purchase period.

I don’t disagree with anything you wrote. My post shows that in the worst possible case, when your money is tied up for 2 years, it’s still worthwhile to participate.

If you have a shorter period than that you’re EVEN BETTER off.

My point is not about shorter holding periods. My point is about the starting “return boost”.

You are saying that ESPP shares start off with a ~10% bonus that you spread over a mandatory holding period, but you should be saying that ESPP shares start off with a much greater boost (92%).

So you’re saying that if there’s a 2-year holding period, you can spread a 92% gain over those 2 years? 1.92^0.5-1=38.6% alpha from the ESPP? That calculation is certainly wrong. Check your math, Jacob!

Ah, you’re right that it’s not correct to spread 92% annualized return over two years, but it still wouldn’t be 10% either. I’d have to do a more complicated calculation.

Found ESPP valuable to net worth, but taxes and commissions certainly drag down the benefit.

Also, found the hassle wasn’t worth it as much when the overall portfolio is more considerable.

If you net 10% after fees/taxes and company limits to 10% of salary:

(Late career) 100k salary yields 1k gain, which barely moves the needle on a 1M portfolio earning 7% (70k)

(Early career) 50k salary yields $500 gain, which does move the needle on 100k portfolio earning 7% (7k)

I found that enforced savings was the larger benefit, and I used ESSP to pay lumpy, infrequent expenses.

ESPP requires labor, so you can think of it as a side job that you can compare to your main job. Summary: an hour of messing with ESPP pays you at least as well as ~4.5 days of your main job.

A) Getting ESPP contributions set up: 5 minutes the very first time. I’ll ignore this small one-time effort.

B) Selling the ESPP stock and moving the money to your normal checking/brokerage account: less than 15 minutes?

C) Figuring out your taxes: If you sell immediately, the ordinary income portion is on your W-2, so it takes a few seconds to enter that data. The real effort is reporting the sales and adjusting the cost basis. Less than 30 minutes?

Assuming the purchase period is 0.5 years, you spend 2*B + C time per year, so an hour?

The benefit is the extra return on 10% of your salary. A 15% discount turns 10% of your salary into 11.8% (and remember you can get a bigger discount), so you benefit at least an extra 1.8% of your salary from an hour’s work. (Yes, I should subtract the expected benefits of investing in the stock market, but that doesn’t change the answer much.)

So, if your salary is $100K, taking advantage of ESPP pays $1800/hour or more while your job only pays you ~$50/hour. Or in more general terms, an hour of messing with ESPP pays at least as much as working ~4.5 days of your job.

This is all pre-taxes.

Good point. With a $1m portfolio there is very little opportunity to create an alpha in the 1% range. But a $1k gain is nothing to sneeze at. Accumulation of small marginal gains is the way to go. You pick up 20 such hacks and now we’re moving! 🙂

Both excellent points, and I agree. Just me being lazy and not appreciating the little wins.

So, if I understood well, so long as you keep the stock purchase plan stock for 2 years only then the portfolio position is improved along the efficient frontier with higher return and lower statistical volatility.

I immagine that, if one keeps the stock longer than two years, then with time the return effect of the discount is gradually diluted and then as the holding period lengthens at some point the extra volatility of holding a single stock will negate the decreasing benefit of the one time discount.

I’m saying all this because what often happened to me is that by the time the two year holding period was over the stock was so loaded with capital gains that I did not want to sell it and incur the significant capital gain. So I would often prefer keeping the stock past 2 years and thus undergoing dilution of the discount benefit with time rather than incur the significant capital gain. So, in the end, those stock lots I acquired during periods of high stock appreciation I ended up being trapped in keeping long term, trapped by the capital gain that is, and waiting for perhaps a low personal income year. Actually, I still have some of those now very appreciated stock lots which I’m stuck with because their tax basis is less than 10% of their value. My total stock position in this one stock is not great but I’m sure it does hurt my diversification a bit. Of course, I’ve been lucky because my company’s stock has generally outperformed the SP 500 by a factor of x2.5 in the last 20 years, so I (retrospectively) wish I had kept more of it as I’m sure the extra performance was worth the extra volatility (but that’s in hindsight only).

Very good point. This is one of the caveats I mentioned: You have to tax your gains along the way.

If your stock went through the roof, +500% or so, you will definitely face a tough decision: should you let the profits run or take/realize the profits and invest in the index. That’s another trade-off, that might take some specialized analysis.

Interesting article.

Over my career I participated in “equivalent” schemes offered by different employers.

I say “equivalent” as I do not reside in the US.

The nuts and bolts were essentially the same across all employers schemes – albeit with slight differences.

The outcomes were wildly different!

However, all outcomes were fundamentally driven by the stock price performance of the employer.

Looking at a sample of three notable employers schemes:

Employer one’s schemes were hugely profitable (to me); employer two’s were a bit mmmmm, and employer three’s schemes were initially very good – but took an absolute hammering due to C-19 – and are now seriously under-water.

On reflection I am glad that I did participate in all of these schemes.

However, I suspect had employer three’s experience been my first experience then I would probably feel very different.

That’s nice of you to share your own experience. It’s in line with what I expected. There is some excess return (but also some risk around it). One single experience can go either way, but once you average over many different years/employers you SHOULD come out ahead! 🙂

Here’s an idea: when my girlfriend worked for Walgreens in 2014 the IRS max was $25,000/year…it was 10% discount with a 90 day mandatory minimum hold before sale. The interesting quirk was that you could call the ESPP 1-800 # AFTER trading had closed and request the purchase and they would give you the most recent closing price. This allowed me to buy a put contract with a strike around 8-9% below where Walgreens stock was trading near the closing bell. I would therefore have virtually no risk in loss on the trade over 90 days because sufficient contracts to cover the $25k would likely cost around a few hundred dollars. I then borrowed the $22,500($25k minus 10% discount) at around 1-2% from Interactive Brokers on margin. I also would collect 2-3% annual dividend during this time and would sell a covered call if the stock happened to rise a good bit over the 90 days and I wanted to reap some extra income…especially if implied volatility and the stock price happened to rise a good bit over the 90 days. The last time I did that…got lucky and my profit was $10k before taxes or so…we used those funds to take a trip to Ireland! I didn’t calculate an IRR, but it was certainly up there on an around 100 day hold period. I thought about how it would be relatively easy to do this for Walgreens employees and make an easy six figures a year with enough clients: $500 fee for 200 clients per year to provide around a $2,000 profit to each client with no capital outlay required on their part. Maybe I will look into the laws/regulations around that sort of thing one of these days. Anyway, thanks for the work you put into the blog! I appreciate it.

Also, I forgot that to maximize efficiency with put coverage I actually did $50k($25k near end of December and $25k near beginning of January)…so the $10k profit was on that larger base…it has been 6 years so I am forgetting the details!

That’s a pretty neat approach. For people on the fence, who are still worried about the risk of holding their company stock this would work beautifully.

Before you advise anyone on this, you should definitely check your state laws. Sounds like you’d need an RIA business with all the licenses, etc.

You should also check your corporate rules. I know that my employer forbids employees ever to make margin trades (puts or calls) on the company stock.

I’ve always participated in ESPP when offered. Yes, I max out my 401-k, FSA, etc. and the decision always came down to whether I invest in ESPP or invest in a taxable account. In determining whether to buy via ESPP, I felt like it more like a options valuation exercise for my company’s stock with the option expiring in 6 months more than anything else because I could sell my stock immediately upon purchase (well usually within a month of purchase since that’s about how long it took to hit my brokerage account). I don’t know how to value options but given the big, fairly stable companies I worked for that offered the ESPPs, the volatility of the stock made it a seem like a no-brainer that I should take that risk for a 15% return in 6 months (assuming the stock price didn’t move). In fact, in one company, the price was actually the lower of the beginning or the end of the 6 month period so my risk of loss was only if the price went down between the month when the price was set and when the stock hit my account and was tradable. Once it was in my account, then I treat it like any other stock holding so whether it was an ESPP purchase or any other stock purchase, it wasn’t relevant anymore.

Good points. The ESPP is likely best when you maxed out everything else tax-advantaged.

And if you get this additional “optionality” of getting the lowest price during the offer period you get even more alpha!

Thanks for sharing!!!