## Contour plots of Sharpe Ratio for various asset mixes

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Topic Author
fundtalker123
Posts: 901
Joined: Tue Feb 27, 2007 4:18 am

### Contour plots of Sharpe Ratio for various asset mixes

I calculated Sharpe Ratio for continuous mixes of stocks (US, International, REITS, Small Cap Value, etc) and bonds (5 year treasury bills) using the 1972-2006 data posted here: http://www.diehards.org/forum/viewtopic ... 9219#29219.

Sharpe ratio is used to estimate portfolio "efficiency" measured by reward to variability (risk) ratio: http://en.wikipedia.org/wiki/Sharpe_ratio
Higher is better (reddest area in each plot is "best")

US Stock vs. EAFE Stock vs. 5 Yr Treasury MIXES:

US Stock - EAFE+EM Stock - 5 Yr Treasury MIXES:

US Stock - US Small Value Stock - 5 Yr Treasury MIXES:

US Stock - REIT - 5 Yr Treasury MIXES:

US Stock - EM Stock - 5 Yr Treasury MIXES:

Do these calculations look right (did I make a mistake)?
* 30-50% stocks (rest bonds) is "good"
* 30-70% EAFE stock tilt is "good"
* 70-100% Small Cap Value tilt is "good"
* 70-100% REIT tilt is "good"
* 60-100% EM tilt, plus ~70% bonds is "good"
Trev H
Posts: 1896
Joined: Fri Mar 02, 2007 10:47 pm

### Morning...

FundTalker...

I have played around with maxing out Sharpe considering using International Market (EAFE/EM) only on the International Side.

If you look at combinations of 500 Index and Intl Market the Sharpe maxes out at around...

60% 500 Index
40% Intl Market
515,464.10 = 10K Growth
11.92 = CAGR
17.10 = StDev
.4243 = Sharpe

If you mix (other asset classes) with Intl Market searching for the highest Sharpe Ratio... you have to go heavy on REIT, SV and a bit of LV.

05% LV
50% REIT
20% SV
25% Intl Market
1,017,482.94 = 10K Growth
14.12 = CAGR
15.34 = StDev
.5981 = Sharpe

10K Growth nearly doubled, with StDev near 3 points lower and Sharpe .17 higher.

I could not find a combination with > 25% Intl Market that pushed the Sharpe Higher considering LV REIT SV combinations on the US Equity Side.

I did not try mixing in InterTerm Treasury but if you do I doubt you will find a much more efficient mix than something similar to this from 1972-2006 using International Market for Intl Exposure.

Fun to look at...

Trev H
Trev H
Posts: 1896
Joined: Fri Mar 02, 2007 10:47 pm

### With 5 Year Treasury Notes

.
Keeping the ratios the same...

30% 500 Index
20% Intl Market
50% InterTerm Treasury
319,644.24
10.41 = CAGR
9.56 = StDev
.5005 = Sharpe

2.5% LV
25% REIT
10% SV
12.5% Intl Market
50% InterTerm Treasury
441,098.31
11.43 = CAGR
8.79 = StDev
.6539 = Sharpe

Trev H
dave.d
Posts: 936
Joined: Mon Mar 19, 2007 10:30 pm
Location: Richmond, VA
This is all great... so long as the next 35 years are a play-by-play replay of the last 35. 95% of equity in REIT, Intl, and SV? Only if the market is drastically inefficient. Color me dubious. This sort of game is a way to lose your shirt.

--Dave
Valuethinker
Posts: 45273
Joined: Fri May 11, 2007 11:07 am
dave.d wrote:This is all great... so long as the next 35 years are a play-by-play replay of the last 35. 95% of equity in REIT, Intl, and SV? Only if the market is drastically inefficient. Color me dubious. This sort of game is a way to lose your shirt.

--Dave
It reminds me, perhaps incorrectly, of how if you plug historic data into a Markowitz optimizer you get an asset allocation which tilts heavily towards 'past favourites'.

Since asset classes have a tendency to mean revert in performance, that usually gives an *underperforming* portfolio in the future.

REITs in particular I would like to see how/where the outperformance has come. REITs were not a big asset class until the ?mid 90s? and they have done very well in the last 10 years.

I don't see where the scope for a further rerating by REITs against common stocks comes from.
stratton
Posts: 11083
Joined: Sun Mar 04, 2007 5:05 pm
Location: Puget Sound
I don't see where the scope for a further rerating by REITs against common stocks comes from.
David Swensen likes them for his suggested portfolio with 20% real estate in a 70/30 portfolio. However, I wouldn't put the entire REIT allocation in the VG REIT Index. I'd diversify into foreign real estate and something like the TIAA Real Esate Product if I had access to it. I'd seriously think about buying a couple of individual timber REITs too.

But, buying the typical REIT index for a huge ~30% of my asset allocation: no!

Paul
Cb
Posts: 275
Joined: Wed Feb 21, 2007 12:39 am
dave.d wrote:This is all great... so long as the next 35 years are a play-by-play replay of the last 35. 95% of equity in REIT, Intl, and SV? Only if the market is drastically inefficient. Color me dubious. This sort of game is a way to lose your shirt.

--Dave
Relax, Dave...I think these guys are just doing "what if's"...have any of them suggested that they'll revamp their portfolios tomorrow? It's a useful tool. It simply demonstrates the benefits of diversification. As Simba explains on the Excel document's README tab:

"Please use this spreadsheet only for learning purposes and as a need for diversification. Don't change your AA purely based on historical returns of a fund.
Past returns are not indicative of future returns."
Topic Author
fundtalker123
Posts: 901
Joined: Tue Feb 27, 2007 4:18 am
I calculated side by side plots of Sharpe and Return (CAGR), and indicated where I am with a black dot. I'm low on bonds (15%) because I'm greedy for high return, and low on international (10%) because I've never been comfortable with it. But the plot suggests lowering bonds and upping international would have lowered risk and increased or maintained high returns. BUT, in the past 35 years international did better than the US. If that reverts, maybe I want to stay where I am (maybe still increase bonds).

Valuethinker
Posts: 45273
Joined: Fri May 11, 2007 11:07 am
stratton wrote:
I don't see where the scope for a further rerating by REITs against common stocks comes from.
David Swensen likes them for his suggested portfolio with 20% real estate in a 70/30 portfolio. However, I wouldn't put the entire REIT allocation in the VG REIT Index. I'd diversify into foreign real estate and something like the TIAA Real Esate Product if I had access to it. I'd seriously think about buying a couple of individual timber REITs too.

But, buying the typical REIT index for a huge ~30% of my asset allocation: no!

Paul
- international REITs are not, by and large, cheaper than American REITs.

There are exceptions (Japan perhaps). And the global upswing in real estate has been so universal, that I suspect historic correlation coefficients will be of less relevance

- timber

Too many people are talking timber, for my taste. And the 'you can't lose' argument that time means trees grow, and hence in value, is also pretty common.

I think the AIM market here is about to have a £250m timber vehicle listing.

Timber *is* interesting. The Chinese are driving demand through the roof. The pine bark beetle in BC has hopped the Rockies and is now killing trees in Alberta.

But travel with care.
Topic Author
fundtalker123
Posts: 901
Joined: Tue Feb 27, 2007 4:18 am

### Effect of Slice-Dice

Here's the effect of using a Slice-Dice on the US Stock portion (20% each of LC, LCV, SC, SCV, REIT)

US Slice-Dice vs. International vs. Bonds (5 yr treasuries)

Same, but with stronger tilt to emerging markets (50% EAFE, 50% EM)

However, be sure to re-read Bogle's Little Book on Common Sense Investing . . .
WWV
Posts: 126
Joined: Fri Feb 23, 2007 8:58 am
Location: Northwest of Chicago

### Just to say

Thanks for posting these plots. I agree with the cautions posted by others-but I do find these representations quite helpful in understanding the relationships.

Bob
"The average investor has only 11,000 more genes than a worm"-New York Times
jms969
Posts: 156
Joined: Tue Feb 20, 2007 5:56 pm
Location: South Central Wisconsin
I want to die peacefully in my sleep like my grandfather, not screaming like the passengers in his car.
Random Musings
Posts: 6248
Joined: Thu Feb 22, 2007 4:24 pm
Location: Pennsylvania
Be interesting to see the same contour plots EOY 1999 - to see what they looked like then.

RM
stratton
Posts: 11083
Joined: Sun Mar 04, 2007 5:05 pm
Location: Puget Sound
Valuethinker wrote: - international REITs are not, by and large, cheaper than American REITs.

There are exceptions (Japan perhaps). And the global upswing in real estate has been so universal, that I suspect historic correlation coefficients will be of less relevance
The one thing going here is most of the foreign real estate isn't in REIT forms. International RE as an investment has been switching to REITs over the last few years and hasn't actually become legally available in countries such as Germany yet. So there is a lot future activity that hasn't happened yet.
Valuethinker wrote:- timber

Too many people are talking timber, for my taste. And the 'you can't lose' argument that time means trees grow, and hence in value, is also pretty common.

I think the AIM market here is about to have a £250m timber vehicle listing.
This is a difficult area from what I can see. There is Plum Creek Timber and Rayonier then a couple of smaller timber REITs. Then there are a couple of companies like Weyerhauser that might turn into REIT. To get any real diversification you need private timber investments, Canroys, and some other foreign timber interests. Expensive and investment quality on some of the players isn't real great.

From what I can tell just buying a tiny bit of PLC and RYN will get most of the market cap in this area, most of the diversification, and the top investment quality. Timber is only around 2% of the REIT market caps so adding timber means over weighting like a SV tilt.

Paul