I don't do any complicated DCF analysis any more. I use Ben Graham's formula instead.

DCF estimates are unavoidably imprecise, at best you can produce some sort of range of reasonable valuations that is still fairly wide. When you are buying a business where most of it's value is based on future earnings growth, to have a strong margin of safety you have to be conservative about DCF assumptions. I do that, and discount heavily.

I'm not looking for a "fair valuation", I'm looking for a valuation that is obviously so cheap it's almost a free-roll for me. A valuation so cheap that if I realize I screwed up my math and forgot to divide it by half, I still didn't overpay.

Apart from pure metrics, what are your main filters in your searching process? I'd appreciate if you have a few pointers on management, owner structure etc (if you could add more nuance than the old and oft repeated Buffett mantras ).

And in special situations, for example bankruptcies, are there any specific factors that would just make you throw your hands up in the air immediately. Conversely, is there anything that would make you put everything else aside at once and start digging away?

How big chunks do bankruptcies and other special situations make up of your portfolio compared to little small cap gems with a consistent track record?

I focus mostly on special situations and bankruptcies in my screening and they are the majority of my holdings.

With bankruptcies if management says the equity is unlikely to have any value and the trading price seems to confirm that, I move on. I have too many ideas to keep digging if I hit concrete in the first few inches. I won't lose sleep if I miss a few long shots.

What makes me excited is if that language is not present and the equity is still trading with the expectation of having value.

Eventually I hope to expand into buying debt as well, which would greatly expand my opportunities in bankruptcy, but right now I'm too busy and like to enter new areas systematically.

This is somewhat a carry over from the other thread, but I figured this was a better place to put it.

What return rate above inflation would you estimate for buy and hold investors using low fee funds? Let's say I have $100k invested now and will be investing 10k every year for the next 30 years. The reason that I ask is that I have a spreadsheet that uses this number to look at my savings going forward. I know it will vary wildly and past doesn't predict future, etc. but someone is better than nothing.

Secondly, do you think DFA funds are worth the fee over Vanguard funds?

DesertCat, in response to your above regarding management not overhyping projections in front of a judge - don't believe that. I am in the "distressed" biz and we deal with a ton of bankrupcies so I have taken a look at a ton of disclosure statements and projections in the ds. Trust me, there is just as much of a chance of management making unjustified hockey stick projections as there is them downplaying their prospects. Be careful there. If you have any questions about the process and buying debt in such companies, shoot me a PM.

Thanks, appreciate the help. I guess I arrived at my conclusion because in the cases I've looked at management is trying to get a ton of options priced very lo, so it seemed like their interests dictated low-balling future potential/valuations. Fortunately I don't rely on assumptions like that, I try to focus on factual data, but when the decision is close incentives can sway me one way or the other.

I actually wrote a much longer post in that thread that got deleted somehow (possibly I didn't post it correctly), but over multiple decades I think you could see as much as 15% per year above inflation/fees, or as low as 5% above (obviously could be zero over a single decade), IF you dollar cost average.

It's amazing how much dollar cost averaging can help you over time.

Couldn't tell you. Despite my conviction the market is often not efficient, I'd have to agree with lots of the EMT criticisms of most active managers. If some firm beats the market over 10 years, is it skill or is it luck? If it's skill, is it a skill that can persist as their funds balloon in size and their investment choices shrink?

I mean I'm pretty sure Bill Miller is an excellent stock picker based on his early career. But his fund grew to such a massive size that it's probably difficult to have more than a minor edge (given mutual fund constraints, not so much in a hedge fund or Berkshire type vehicle). Given his results have sucked so badly since does it mean I'm wrong, or did the type of investing change to one he has little skill at (macro driven large cap predictions)?

Do you really need at least 10k to start investing?

No, it depends on your goals. I started dabbling with less, got more serious over time and added money to my account. Transaction costs may be proprtionately higher in a small account, but typically they are low enough nowadays at a discount broker it's not a big difference. The earlier you start and pay your tuition, the better.

I realized that maybe I should have posted this here since I'm addressing Desert Cat:

One more question about this: I would think that a good model for how a buy and hold-er invests is that they invest over a 30 year period and then withdraw over a 30 year period. But I would think this would be the same as looking at a set of 30 year investments and then you could average them. Isn't that what is being done in this graphic when they come up with 4.1% rate of return?

Where does my thinking betray me?

Note that I am talking about being 100% invested in stocks which I agree is not common, but it still seems odd that DCA would be vastly different than the average I refer to above.

We are talking about this chart, correct?

Remember, their 4.1% rate of return is after tax/inflation/fees, so it's probably a raw return of 8-9%. And it doesn't incorporate any dollar cost averaging, it's pretty clear that each square is the return from fixed investment amount from a start year to an end year. Read the example text ("if you invested money at the end of 1930 and withdrew it in 1950");

To incorporate dollar cost averaging, they'd have to increment the investment size each year and use a variable unit for each years increment, i.e. more units when market is down, and fewer when it's up.

Pretty clearly their chart would show higher returns in almost every square if they incorporated dollar cost averaging into their model. The only time that DCA can produce worse returns than lump sum is if the market index is very low when you start, quickly rises and stays much higher during the duration of your investment period. Then you are putting in the bulk of your investment at higher prices, and missed the opportunity to put it in as a lump sum at the most attractive price.

But that scenario is extremely unrealistic for almost everyone, since they usually don't start saving for retirement with a large lump sum, and even if they do will continue to add to the investment over decades.

With regards to DCA (I'll come back to my other question after I do some simulation work), if I had 5 million dollars in cash at age 30 and was never planning on earning another dollar in my life, are you saying that I would (on average) end up with more money at age 60 I invested that over 30 years rather than putting it all in immediately?

I think (on average) you would be better off lump-summing your investment. However, if 5 million is all you have, and you don't plan on earning anymore, I'd think you would want to DCA just to be safe. I think you are playing not to lose here instead of playing to win.

But like DC says, this situation is extremely rare. Most people when they start investing put some money in and then just keep adding to it over time.

DC -- I would be interested in how you would invest an unexpected windfall, such as an inheritance (for the average investor going into mutual funds, not someone like you who cold hold cash for the right opportunity). Would you just throw it all in at once or DCA?

For a passive investor it depends on their timeframe. If you aren't going to touch it for thirty years putting most into index funds right away is probably the highest return option. Trying to use DCA in that scenario means keeping a ton of the portfolio in lower yielding money market or bond funds for a few years and that's naturally going to lower long term returns.

More realistically you need to think about utility. If you get a good sized inheritance, you will want to spend some well before retirement, and reducing variance and risk becomes more important than maximizing long term returns, because you are much closer to your goals. You don't want to backslide, so I'd probably recommend half low risk bond funds to lower variance and generate spendable income, and half equities to keep pace with inflation.

Thanks for the reply, and I agree completely!

Can you explain how the chart would show higher returns fi they incorporated dollar cost averaging? It is not clear to me.

You should look up dollar cost averaging. It lowers your average purchase price over time because when the market is lower, you get more units of the market, and when it's higher, you get fewer.

Now since usually the market is much lower decades ago, it seems as if you get the best price putting it in at the beginning of a long investment period. You certainly get the highest nominal returns, i.e. your investment increases in size more. But DCA has half the holding period. So when you compare a 40 year lump sum investment to DCA, DCA only has a 20 year average holding period so it's lower average purchase price can lead to higher annualized returns.

In reality, they are two different things. If you had $1M you wanted to invest for 40 years at the highest return possible you'd usually just put the whole amount to work. But people typically invest over time, and get the benefits of DCA naturally, and people who put together charts together on long term stock market returns should know this.

I know about DCA (at least the basics). However I do not believe that you can just take the investment time and average it. If you invest $100 30 years ago and let it compound over time and then invest $100 yesterday, if you average the time invested it will show a higher return than just investing the money 30 years ago. This doesn't make any sense. I found the following website on calculating annualized returns when using DCA: http://www.financems.com/how-to-calc...averaging.html.

I wrote a simulation that generates a random number with a mean and SD for the return rate for that year. I ran it with DCA and calculated the annualized return using the formula on that website (which I agree with). I then ran it with a lump sum and it generated the same annualized return.

I agree there are other advantages to DCA and the fact that you receive money throughout your life makes DCA something that is done. However I don't believe that it increases your annualized return.

Your simulation is wrong, either you misprogrammed it or misunderstood the math. DCA shouldn't ever generate the same annualized return as a lump sum.

And it increases your return by lowering your average basis. Think of it this way. You can invest $300 in a lump sum to buy 3 units at $100 each, the units trade over 3 consecutive years at the prices $75, $200, $300. Or you can invest $100 per year at the prevailing price. You buy 1 unit the first year, 1.33 units the second, and 0.5 units the third. The results works like this.

Lump sum: $300 invested for 3 units, $900 returned over 3 year average holding period.
DCA: $300 invested invested for 2.83 units, $849 returned over 2 year average holding period.

Which is the higher return?

Each square is worth the same investment amount so if you want to look at the effects of dollar cost averaging you would take each individual box that matches the years of deposit and withdrawal and you would weight them based on the length of time held to see the average annual rate.

I'm pretty positive that you can't just average the holding periods. I'll work through the scenario I mentioned in my previous post:

Invest $100 50 years ago in something that averages a 5% annualized return. You end up with $1147 for a return of 11.5x and the obvious annualized return of 5% [calculated (11.5)^(1/50)-1].

Now you do the same thing, but yesterday you buy another $100 of it. Now you've invested $200 so your return is is 5.7x, but if you say your investment period is only 25 years your annualized rate becomes (5.7)^(1/25)-1 = 7.2% which does not make sense.

I think the mistake is that we are both using dollars, which change with investment returns, instead of units of investment.

In your example you buy 1 unit for $100 50 years ago. Yesterday you invest another $100, which only buys you 100/1147 units. You own 1.087 units worth $1247 at a total cost of $200, and an averaging holding period of 46 years per unit. Your annualized return is 4.2%, which makes much more sense given that for a short period half of the portfolio had a zero return, so the answer should be a lower return.

Let's redo my DCA investment with that in mind.

We invest $300 in a lump sum to buy 3 units at $100 each the first year, hold them 3 years, so our averaging holding period is 3 years per unit, and sell at $300 per unit, or $900 total, for a 200% gain over 3 years or 44.2% annualized.

Or we can dollar cost average buying $100 of units over 3 consecutive years. at the prices $75, $200, $300. We buy 1 unit the first year at $100, 1.33 units the second at $75, and 0.5 units the third at $200. The same $300 is invested for 2.83 units, $849 total. The average holding period on a per unit basis is 1 unit at 3 years, plus 1.33 units at 2 years plus 0.5 units at 1 year, added up and divided by 2.83 units equals an average holding period of 2.17 years, and produces a return 61.8% annualized.

Looking at the DCA estimates I did from Schiller's data it appears I made the same mistake, and probably over-stated the benefits of DCA. But the benefits are still there. I'll redo the math and repost it.

Ok, in the example where the chart claimed that the market 1966-2009 slightly trailed inflation. Ignoring dividends like the chart did, the S&P increased from 93.32 to 757.13 from Jan. 1966 to March 2009 over 43.25 years, an increase of 8.11x and an annualized rate of 4.96%.

Calculated with a single lump sum invested at the beginning with dividends reinvested produces an increase of 24.19x, and an annualized return of 7.64%.

I then calculated with a fixed amount invested monthly, and dividends reinvested, by buying units of the S&P each month with the fixed amount + dividends on existing units and adding it to the existing units owned. To estimate the average holding period I sum the units owned every month, creating a sum of unit months during the period. Then I divided by units and 12 to get the average holding period of 22.96 years.

The investment increase of 10.46x over 22.96 years, produces an annualized return of 10.76%.

Yeah, I could see averaging by units. That makes more sense.

On your example, why does DCA get to buy at $75 the first year but lump sum has to buy at $100?

$100 is the start year, they both pay that price initially, $75 is year 2. But it doesn't always have to be lower, let's do it with every year higher than the first, i.e. $100, $150, $200, and finishing at $300.

DCA buys 1 unit, .67 units, .5 units for 2.17 units total, and an average holding period of 3 + 1.33 + .5 unit years, or 4.83/2.17 = 2.25 years. Total return is 2.17x over 2.25 years or 41% annualized.

Lump sum is the same 44%, so DCA slightly trails in this example. But it also shows you how hard it is to find examples where DCA trails, essentially the market has to go up and up and never retrench or even flatten for lump sum to win.

For example let's do it again with one minor tweak in making year 3 $150 just like year 2. Now DCA buys 1 unit, .67 units, & .67 units for 2.33 units total. Averaging holding period is 3 + 1.33 + .67 = 5/2.33 = 2.14 years. Total return is 700/300^2.14 or 48.6% annualized.

DCA often wins even when the market doesn't drop during the investment periods, because the fluctuations and flat points mean that the annualized returns from those points often exceed the returns from the beginning point. I think the worst market for DCA vs. lump sum would be one where the first year returns are the highest in the series, and the rest of the series still offers positive returns but small ones.

But in the end it's a meaningless "competition", we rarely if ever choose between investing via DCA and lump sum. It's just nice to know that DCA offers great benefits to passive investors over long periods in almost every market.